de Grey Graphs

Author

Eric W. Weisstein
July 20, 2023

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/deGreyGraphs.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/deGreyGraphs.html.

©2023 Wolfram Research, Inc. except for portions noted otherwise

Table

TextGrid[Sort[GraphData[#,{"VertexCount","EdgeCount","ChromaticNumber","#"}]&/@GraphData["DeGrey*"]],Dividers->All,Alignment->{{{Decimal},Left}}]

"DeGreyGraph59"

de Grey, A. and Haugstrup, A.  "Two small 6-chromatic unit-distance graphs in R."  Geocombinatorics 30, 5–13, 2020.

Construction

The final step is to note that each clamp can rotate freely about its clamped axis. Thus, we can merge one pair of points by (for example) rotating each of the x-axis and y-axis clamps so that one of their north poles sits on the plane x = y. By symmetry, clearly the z-coordinates of those two points will be equal. Thus, finally we obtain a (messy, so not shown) 59-vertex UDG in R3 that cannot be 5-coloured.

The rotation is pretty easy to describe, because each clamp attaches to points ± 1/Sqrt[2] on one axis and zero on the others, so their rotations are about the coordinate axes. Call them the x-clamp, the y-clamp and the z-clamp. Then, taking the coordinates I give in the paper, wlog assume that the vertex of each clamp that is the clamp’s flap vertex is the one whose non-zero coordinate is positive. OK, so take any vertex in the x-clamp whose x-coordinate is less than its y-coordinate. We can then rotate that clamp around the x-axis, and each of its vertices traces a circle with x unchanging, so we can get our chosen vertex to a point on the x=y plane. Then take the same vertex (or the one that is its reflection in x=0) from the y-clamp and rotate the clamp so that it too is in the x=y plane. Then they coincide.

clamps={{{(NumericalApproximation[Root, (RowDefault["0.0986", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,3], ]),(NumericalApproximation[Root, (RowDefault["-0.619", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ])},{(NumericalApproximation[Root, (RowDefault["-0.0986", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.619", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ])},{(NumericalApproximation[Root, (RowDefault["0.186", FEExpressionsNumericalApproximationElider]), Root[-49039671+185779840 #1+398463200 ((#1)^2)+94976000 ((#1)^3)+7840000 ((#1)^4)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.975", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,1], ]),(5/(6 (Sqrt[2])))},{(NumericalApproximation[Root, (RowDefault["-0.186", FEExpressionsNumericalApproximationElider]), Root[-49039671-185779840 #1+398463200 ((#1)^2)-94976000 ((#1)^3)+7840000 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.975", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,1], ]),(5/(6 (Sqrt[2])))},{(NumericalApproximation[Root, (RowDefault["0.258", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,4], ]),(NumericalApproximation[Root, (RowDefault["-0.918", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-0.258", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.918", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ])},{(NumericalApproximation[Root, (RowDefault["0.457", FEExpressionsNumericalApproximationElider]), Root[-71412783+28501280 #1+317218400 ((#1)^2)-85568000 ((#1)^3)+7840000 ((#1)^4)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.208", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,4], ]),(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ])},{(NumericalApproximation[Root, (RowDefault["-0.457", FEExpressionsNumericalApproximationElider]), Root[-71412783-28501280 #1+317218400 ((#1)^2)+85568000 ((#1)^3)+7840000 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.208", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,4], ]),(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ])},{(NumericalApproximation[Root, (RowDefault["0.465", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,3], ]),(NumericalApproximation[Root, (RowDefault["-0.420", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ])},{(NumericalApproximation[Root, (RowDefault["-0.465", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.420", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ])},{(NumericalApproximation[Root, (RowDefault["0.486", FEExpressionsNumericalApproximationElider]), Root[-71412783-28501280 #1+317218400 ((#1)^2)+85568000 ((#1)^3)+7840000 ((#1)^4)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.125", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ])},{(NumericalApproximation[Root, (RowDefault["-0.486", FEExpressionsNumericalApproximationElider]), Root[-71412783+28501280 #1+317218400 ((#1)^2)-85568000 ((#1)^3)+7840000 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.125", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ])},{(1/2),(NumericalApproximation[Root, (RowDefault["-1.42", FEExpressionsNumericalApproximationElider]), Root[-4821911-17325288 ((#1)^2)+9809424 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.0120", FEExpressionsNumericalApproximationElider]), Root[9-62516 ((#1)^2)+68121 ((#1)^4)&,3], ])},{-(1/2),(NumericalApproximation[Root, (RowDefault["-1.42", FEExpressionsNumericalApproximationElider]), Root[-4821911-17325288 ((#1)^2)+9809424 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.0120", FEExpressionsNumericalApproximationElider]), Root[9-62516 ((#1)^2)+68121 ((#1)^4)&,3], ])},{(1/(Sqrt[2])),0,0},{-(1/(Sqrt[2])),0,0},{(NumericalApproximation[Root, (RowDefault["0.757", FEExpressionsNumericalApproximationElider]), Root[-49039671-185779840 #1+398463200 ((#1)^2)-94976000 ((#1)^3)+7840000 ((#1)^4)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.643", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,2], ]),(5/(6 (Sqrt[2])))},{(NumericalApproximation[Root, (RowDefault["-0.757", FEExpressionsNumericalApproximationElider]), Root[-49039671+185779840 #1+398463200 ((#1)^2)+94976000 ((#1)^3)+7840000 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.643", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,2], ]),(5/(6 (Sqrt[2])))},{(NumericalApproximation[Root, (RowDefault["0.777", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,4], ]),(NumericalApproximation[Root, (RowDefault["-0.553", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-0.777", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.553", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ])}},


{{(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ]),(NumericalApproximation[Root, (RowDefault["0.0986", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,3], ]),(NumericalApproximation[Root, (RowDefault["-0.619", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ])},{(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ]),(NumericalApproximation[Root, (RowDefault["-0.0986", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.619", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ])},{(5/(6 (Sqrt[2]))),(NumericalApproximation[Root, (RowDefault["0.186", FEExpressionsNumericalApproximationElider]), Root[-49039671+185779840 #1+398463200 ((#1)^2)+94976000 ((#1)^3)+7840000 ((#1)^4)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.975", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,1], ])},{(5/(6 (Sqrt[2]))),(NumericalApproximation[Root, (RowDefault["-0.186", FEExpressionsNumericalApproximationElider]), Root[-49039671-185779840 #1+398463200 ((#1)^2)-94976000 ((#1)^3)+7840000 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.975", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.258", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,4], ]),(NumericalApproximation[Root, (RowDefault["-0.918", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.258", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.918", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ])},{(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ]),(NumericalApproximation[Root, (RowDefault["0.457", FEExpressionsNumericalApproximationElider]), Root[-71412783+28501280 #1+317218400 ((#1)^2)-85568000 ((#1)^3)+7840000 ((#1)^4)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.208", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,4], ])},{(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ]),(NumericalApproximation[Root, (RowDefault["-0.457", FEExpressionsNumericalApproximationElider]), Root[-71412783-28501280 #1+317218400 ((#1)^2)+85568000 ((#1)^3)+7840000 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.208", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,4], ])},{(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ]),(NumericalApproximation[Root, (RowDefault["0.465", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,3], ]),(NumericalApproximation[Root, (RowDefault["-0.420", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ])},{(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ]),(NumericalApproximation[Root, (RowDefault["-0.465", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.420", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ])},{(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ]),(NumericalApproximation[Root, (RowDefault["0.486", FEExpressionsNumericalApproximationElider]), Root[-71412783-28501280 #1+317218400 ((#1)^2)+85568000 ((#1)^3)+7840000 ((#1)^4)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.125", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,2], ])},{(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ]),(NumericalApproximation[Root, (RowDefault["-0.486", FEExpressionsNumericalApproximationElider]), Root[-71412783+28501280 #1+317218400 ((#1)^2)-85568000 ((#1)^3)+7840000 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.125", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,2], ])},{(NumericalApproximation[Root, (RowDefault["0.0120", FEExpressionsNumericalApproximationElider]), Root[9-62516 ((#1)^2)+68121 ((#1)^4)&,3], ]),(1/2),(NumericalApproximation[Root, (RowDefault["-1.42", FEExpressionsNumericalApproximationElider]), Root[-4821911-17325288 ((#1)^2)+9809424 ((#1)^4)&,1], ])},{(NumericalApproximation[Root, (RowDefault["0.0120", FEExpressionsNumericalApproximationElider]), Root[9-62516 ((#1)^2)+68121 ((#1)^4)&,3], ]),-(1/2),(NumericalApproximation[Root, (RowDefault["-1.42", FEExpressionsNumericalApproximationElider]), Root[-4821911-17325288 ((#1)^2)+9809424 ((#1)^4)&,1], ])},{0,(1/(Sqrt[2])),0},{0,-(1/(Sqrt[2])),0},{(5/(6 (Sqrt[2]))),(NumericalApproximation[Root, (RowDefault["0.757", FEExpressionsNumericalApproximationElider]), Root[-49039671-185779840 #1+398463200 ((#1)^2)-94976000 ((#1)^3)+7840000 ((#1)^4)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.643", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,2], ])},{(5/(6 (Sqrt[2]))),(NumericalApproximation[Root, (RowDefault["-0.757", FEExpressionsNumericalApproximationElider]), Root[-49039671+185779840 #1+398463200 ((#1)^2)+94976000 ((#1)^3)+7840000 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.643", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,2], ])},{(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.777", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,4], ]),(NumericalApproximation[Root, (RowDefault["-0.553", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.777", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.553", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ])}},

{{(NumericalApproximation[Root, (RowDefault["-0.619", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ]),(NumericalApproximation[Root, (RowDefault["0.0986", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,3], ])},{(NumericalApproximation[Root, (RowDefault["-0.619", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ]),(NumericalApproximation[Root, (RowDefault["-0.0986", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,2], ])},{(NumericalApproximation[Root, (RowDefault["-0.975", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,1], ]),(5/(6 (Sqrt[2]))),(NumericalApproximation[Root, (RowDefault["0.186", FEExpressionsNumericalApproximationElider]), Root[-49039671+185779840 #1+398463200 ((#1)^2)+94976000 ((#1)^3)+7840000 ((#1)^4)&,2], ])},{(NumericalApproximation[Root, (RowDefault["-0.975", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,1], ]),(5/(6 (Sqrt[2]))),(NumericalApproximation[Root, (RowDefault["-0.186", FEExpressionsNumericalApproximationElider]), Root[-49039671-185779840 #1+398463200 ((#1)^2)-94976000 ((#1)^3)+7840000 ((#1)^4)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-0.918", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.258", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,4], ])},{(NumericalApproximation[Root, (RowDefault["-0.918", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.258", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,1], ])},{(NumericalApproximation[Root, (RowDefault["0.208", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,4], ]),(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ]),(NumericalApproximation[Root, (RowDefault["0.457", FEExpressionsNumericalApproximationElider]), Root[-71412783+28501280 #1+317218400 ((#1)^2)-85568000 ((#1)^3)+7840000 ((#1)^4)&,2], ])},{(NumericalApproximation[Root, (RowDefault["0.208", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,4], ]),(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ]),(NumericalApproximation[Root, (RowDefault["-0.457", FEExpressionsNumericalApproximationElider]), Root[-71412783-28501280 #1+317218400 ((#1)^2)+85568000 ((#1)^3)+7840000 ((#1)^4)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-0.420", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ]),(NumericalApproximation[Root, (RowDefault["0.465", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,3], ])},{(NumericalApproximation[Root, (RowDefault["-0.420", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ]),(NumericalApproximation[Root, (RowDefault["-0.465", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,2], ])},{(NumericalApproximation[Root, (RowDefault["-0.125", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ]),(NumericalApproximation[Root, (RowDefault["0.486", FEExpressionsNumericalApproximationElider]), Root[-71412783-28501280 #1+317218400 ((#1)^2)+85568000 ((#1)^3)+7840000 ((#1)^4)&,2], ])},{(NumericalApproximation[Root, (RowDefault["-0.125", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ]),(NumericalApproximation[Root, (RowDefault["-0.486", FEExpressionsNumericalApproximationElider]), Root[-71412783+28501280 #1+317218400 ((#1)^2)-85568000 ((#1)^3)+7840000 ((#1)^4)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-1.42", FEExpressionsNumericalApproximationElider]), Root[-4821911-17325288 ((#1)^2)+9809424 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.0120", FEExpressionsNumericalApproximationElider]), Root[9-62516 ((#1)^2)+68121 ((#1)^4)&,3], ]),(1/2)},{(NumericalApproximation[Root, (RowDefault["-1.42", FEExpressionsNumericalApproximationElider]), Root[-4821911-17325288 ((#1)^2)+9809424 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.0120", FEExpressionsNumericalApproximationElider]), Root[9-62516 ((#1)^2)+68121 ((#1)^4)&,3], ]),-(1/2)},{0,0,(1/(Sqrt[2]))},{0,0,-(1/(Sqrt[2]))},{(NumericalApproximation[Root, (RowDefault["-0.643", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,2], ]),(5/(6 (Sqrt[2]))),(NumericalApproximation[Root, (RowDefault["0.757", FEExpressionsNumericalApproximationElider]), Root[-49039671-185779840 #1+398463200 ((#1)^2)-94976000 ((#1)^3)+7840000 ((#1)^4)&,2], ])},{(NumericalApproximation[Root, (RowDefault["-0.643", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,2], ]),(5/(6 (Sqrt[2]))),(NumericalApproximation[Root, (RowDefault["-0.757", FEExpressionsNumericalApproximationElider]), Root[-49039671+185779840 #1+398463200 ((#1)^2)+94976000 ((#1)^3)+7840000 ((#1)^4)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-0.553", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.777", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,4], ])},{(NumericalApproximation[Root, (RowDefault["-0.553", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.777", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,1], ])}}};

clamps[[1]][[15]]

clamps[[2]][[15]]

Try a point in the x - clamp with x coordinate < y - coordinate:

pts=Position[clamps[[1]],_?(#[[1]]<#[[2]]&),1,Heads->False]//Flatten

pts=Position[clamps[[1]],_?(#[[1]]>#[[2]]&),1,Heads->False]//Flatten

Point 1

pt=1;

qx=q/.Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]//RootReduce

N[qx]

Find the corresponding angle to rotate the y-clamp so that its first point has x == y:

qy=q/.Solve[Equal@@Take[RotationMatrix[q,{0,1,0}].clamps[[2,pt]],2]&&0<q<2π,q]//RootReduce

N[qy]

Manipulate[Show[
Graphics3D[{
Red,Thick,Line[{{0,0,0},RotationMatrix[q1,{1,0,0}].clamps[[1,1]]}],
Blue,Thickness[.02],Line[{{0,0,0},RotationMatrix[q2,{0,1,0}].clamps[[2,1]]}]
},PlotRange->1,Axes->True,AxesOrigin->{0,0,0},AxesLabel->{x,y,z},Ticks->None],
ContourPlot3D[x==y,{x,-1,1},{y,-1,1},{z,-1,1}]],
{{q1,qx[[1]]},0.,2π},{{q2,qy[[2]]},0.,2π}]

clamp1=RotationMatrix[qx[[1]],{1,0,0}].#&/@clamps[[1]];
clamp2=RotationMatrix[qy[[2]],{0,1,0}].#&/@clamps[[2]];
clamp3=clamps[[3]];

vnew=Join[clamp1,clamp2,clamp3];

g60withrotatedclamps=Graph[Range[60],UnitEdges[vnew],VertexCoordinates->vnew,
EdgeStyle->Join[
Thread[UnitEdges[clamp1]->Red],
Thread[(UnitEdges[clamp2]/.i_Integer:>i+20)->Green],
Thread[(UnitEdges[clamp3]/.i_Integer:>i+40)->Blue]],VertexStyle->Join[Thread[Range[20]->Red],Thread[Range[21,40]->Green],Thread[Range[41,60]->Blue]],
VertexLabels->Automatic,Axes->True,AxesOrigin->{0,0,0},AxesStyle->Directive[Black,Thick],AxesLabel->{"x","y","z"},Ticks->None]

EdgeCount[g60withrotatedclamps]

v60=GraphEmbedding[g60withrotatedclamps];

N[v60[[pt]]-v60[[20+pt]],100]

edges=List@@@EdgeList[g60withrotatedclamps]

Select[SortBy[{#/.i_Integer:>Which[i==21,1,i>21,i-1,True,i],#}&/@edges,First],!MatchQ[-Subtract@@#,{1,1}|{0,0}|{0,1}]&]

Length[%]

P

g59=IndexGraph@VertexContract[g60withrotatedclamps,{pt,20+pt}]

VertexCount[g59]

UnitDistanceGraphEmbeddingQ[g59]

EdgeCount[g59]

UnitEdges[GraphEmbedding@g59]===EdgeList@g59

VertexChromaticNumber[g59]

IsomorphicGraphQ[g59,ContractCoincidentVertices[g59]]

Point 2

clamps[[1]][[15]]

Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,2]],2]&&0<q<2π,q]//RootReduce

N[%]

clamps[[2]][[15]]

Find the corresponding angle to rotate the y-clamp so that its first point has x == y:

Solve[Equal@@Take[RotationMatrix[q,{0,1,0}].clamps[[2,2]],2]&&0<q<2π,q]//RootReduce

N[%]

Manipulate[Show[
Graphics3D[{
Red,Thick,Line[{{0,0,0},RotationMatrix[q1,{1,0,0}].clamps[[1,2]]}],
Blue,Thickness[.02],Line[{{0,0,0},RotationMatrix[q2,{0,1,0}].clamps[[2,2]]}]
},PlotRange->1,Axes->True,AxesOrigin->{0,0,0},AxesLabel->{x,y,z},Ticks->None],
ContourPlot3D[x==y,{x,-1,1},{y,-1,1},{z,-1,1}]],
{{q1,1.5275960982737375`},0.,2π},{{q2,0.2745010705751584`},0.,2π}]

clamp1=RotationMatrix[-2 ArcTan[(NumericalApproximation[Root, (RowDefault["-0.958", FEExpressionsNumericalApproximationElider]), Root[1653600598763063535777699225911803178249415009021249+33060045056547539096905576002347700569734211145628800 ((#1)^2)+314682039675202802478126963106648213861393018825663092 ((#1)^4)-3223243043920653026210410953698616735944418500524322400 ((#1)^6)+«12»+2684190862453850597207315866330318561945619955998816195322 ((#1)^24)-1932722402173111165694292514513323391287678132994610242400 ((#1)^26)+1025110899525700443650630989140693637741915890029394818292 ((#1)^28)-439035177598402440518427751131256381569768047158151635200 ((#1)^30)+142653415827556657440185810354966774292120310354700960449 ((#1)^32)&,2], ])],{1,0,0}].#&/@clamps[[1]];
clamp2=RotationMatrix[2 ArcTan[(NumericalApproximation[Root, (RowDefault["0.138", FEExpressionsNumericalApproximationElider]), Root[23862012361374189759105462965437919055901476387653332031-1234865620094605392407796511606792673461493429322462553600 #1+4235514598318226779914148853399821669308618177764595734288 ((#1)^2)+«39»+107545384148708945892422166037976407742214936188190699507200 ((#1)^29)+4235514598318226779914148853399821669308618177764595734288 ((#1)^30)-1234865620094605392407796511606792673461493429322462553600 ((#1)^31)+23862012361374189759105462965437919055901476387653332031 ((#1)^32)&,4], ])],{0,1,0}].#&/@clamps[[2]];
clamp3=clamps[[3]];

vnew=Join[clamp1,clamp2,clamp3];

g60withrotatedclamps=Graph[Range[60],UnitEdges[vnew],VertexCoordinates->vnew,
EdgeStyle->Join[
Thread[UnitEdges[clamp1]->Red],
Thread[(UnitEdges[clamp2]/.i_Integer:>i+20)->Green],
Thread[(UnitEdges[clamp3]/.i_Integer:>i+40)->Blue]],VertexStyle->Join[Thread[Range[20]->Red],Thread[Range[21,40]->Green],Thread[Range[41,60]->Blue]],VertexLabels->Automatic,Axes->True,AxesOrigin->{0,0,0},AxesStyle->Directive[Black,Thick],AxesLabel->{"x","y","z"},Ticks->None]

v60=GraphEmbedding[g60withrotatedclamps];

N[v60[[2]]-v60[[20+2]],100]

g59=IndexGraph@VertexContract[g60withrotatedclamps,{2,20+2}]

VertexCount[g59]

UnitDistanceGraphEmbeddingQ[g59]

EdgeCount[g59]

VertexChromaticNumber[g59]

Point 3

clamps[[1]][[15]]

Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,3]],2]&&0<q<2π,q]//RootReduce

N[%]

clamps[[2]][[15]]

Find the corresponding angle to rotate the y-clamp so that its first point has x == y:

Solve[Equal@@Take[RotationMatrix[q,{0,1,0}].clamps[[2,3]],2]&&0<q<2π,q]//RootReduce

N[%]

Manipulate[Show[
Graphics3D[{
Red,Thick,Line[{{0,0,0},RotationMatrix[q1,{1,0,0}].clamps[[1,3]]}],
Blue,Thickness[.02],Line[{{0,0,0},RotationMatrix[q2,{0,1,0}].clamps[[2,3]]}]
},PlotRange->1,Axes->True,AxesOrigin->{0,0,0},AxesLabel->{x,y,z},Ticks->None],
ContourPlot3D[x==y,{x,-1,1},{y,-1,1},{z,-1,1}]],
{{q1,2.2783864544860806`},0.,2π},{{q2,0.3792807041209718`},0.,2π}]

clamp1=RotationMatrix[-2 ArcTan[(NumericalApproximation[Root, (RowDefault["-2.17", FEExpressionsNumericalApproximationElider]), Root[3222775992685365871064657999473717921-291312171718664240048007125481967400000 ((#1)^2)+2698535943660507364491509374330781570868 ((#1)^4)-10091345719523467675167858788458420300000 ((#1)^6)+23707788858056270534387880820647673660538 ((#1)^8)-45536092398571478565077070419539557900000 ((#1)^10)+«9»+23707788858056270534387880820647673660538 ((#1)^24)-10091345719523467675167858788458420300000 ((#1)^26)+2698535943660507364491509374330781570868 ((#1)^28)-291312171718664240048007125481967400000 ((#1)^30)+3222775992685365871064657999473717921 ((#1)^32)&,2], ])],{1,0,0}].#&/@clamps[[1]];
clamp2=RotationMatrix[2 ArcTan[(NumericalApproximation[Root, (RowDefault["0.192", FEExpressionsNumericalApproximationElider]), Root[3087675992402281510669323492676719938401-166800319001136862985190841910866333716752 ((#1)^2)+442932882415738085907191459503933286935416 ((#1)^4)+46111618653714579535553457558862509140161232 ((#1)^6)+«14»+168368482416978975486122498702017935486583196 ((#1)^24)+46111618653714579535553457558862509140161232 ((#1)^26)+442932882415738085907191459503933286935416 ((#1)^28)-166800319001136862985190841910866333716752 ((#1)^30)+3087675992402281510669323492676719938401 ((#1)^32)&,10], ])],{0,1,0}].#&/@clamps[[2]];
clamp3=clamps[[3]];

vnew=Join[clamp1,clamp2,clamp3];

g60withrotatedclamps=Graph[Range[60],UnitEdges[vnew],VertexCoordinates->vnew,
EdgeStyle->Join[
Thread[UnitEdges[clamp1]->Red],
Thread[(UnitEdges[clamp2]/.i_Integer:>i+20)->Green],
Thread[(UnitEdges[clamp3]/.i_Integer:>i+40)->Blue]],VertexStyle->Join[Thread[Range[20]->Red],Thread[Range[21,40]->Green],Thread[Range[41,60]->Blue]],VertexLabels->Automatic,Axes->True,AxesOrigin->{0,0,0},AxesStyle->Directive[Black,Thick],AxesLabel->{"x","y","z"},Ticks->None]

v60=GraphEmbedding[g60withrotatedclamps];

N[v60[[3]]-v60[[20+3]],100]

g59=IndexGraph@VertexContract[g60withrotatedclamps,{3,20+3}]

VertexCount[g59]

UnitDistanceGraphEmbeddingQ[g59]

EdgeCount[g59]

VertexChromaticNumber[g59]

Point 4

clamps[[1]][[15]]

pt=4;

Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]//RootReduce

N[%]

clamps[[2]][[15]]

Find the corresponding angle to rotate the y-clamp so that its first point has x == y:

Solve[Equal@@Take[RotationMatrix[q,{0,1,0}].clamps[[2,pt]],2]&&0<q<2π,q]//RootReduce

N[%]

Manipulate[Show[
Graphics3D[{
Red,Thick,Line[{{0,0,0},RotationMatrix[q1,{1,0,0}].clamps[[1,pt]]}],
Blue,Thickness[.02],Line[{{0,0,0},RotationMatrix[q2,{0,1,0}].clamps[[2,pt]]}]
},PlotRange->1,Axes->True,AxesOrigin->{0,0,0},AxesLabel->{x,y,z},Ticks->None],
ContourPlot3D[x==y,{x,-1,1},{y,-1,1},{z,-1,1}]],
{{q1,1.9500770309158684`},0.,2π},{{q2,0.7075901276911839`},0.,2π}]

clamp1=RotationMatrix[-2 ArcTan[(NumericalApproximation[Root, (RowDefault["-1.48", FEExpressionsNumericalApproximationElider]), Root[3222775992685365871064657999473717921-291312171718664240048007125481967400000 ((#1)^2)+2698535943660507364491509374330781570868 ((#1)^4)-10091345719523467675167858788458420300000 ((#1)^6)+23707788858056270534387880820647673660538 ((#1)^8)-45536092398571478565077070419539557900000 ((#1)^10)+«9»+23707788858056270534387880820647673660538 ((#1)^24)-10091345719523467675167858788458420300000 ((#1)^26)+2698535943660507364491509374330781570868 ((#1)^28)-291312171718664240048007125481967400000 ((#1)^30)+3222775992685365871064657999473717921 ((#1)^32)&,3], ])],{1,0,0}].#&/@clamps[[1]];
clamp2=RotationMatrix[2 ArcTan[(NumericalApproximation[Root, (RowDefault["0.369", FEExpressionsNumericalApproximationElider]), Root[3087675992402281510669323492676719938401-166800319001136862985190841910866333716752 ((#1)^2)+442932882415738085907191459503933286935416 ((#1)^4)+46111618653714579535553457558862509140161232 ((#1)^6)+«14»+168368482416978975486122498702017935486583196 ((#1)^24)+46111618653714579535553457558862509140161232 ((#1)^26)+442932882415738085907191459503933286935416 ((#1)^28)-166800319001136862985190841910866333716752 ((#1)^30)+3087675992402281510669323492676719938401 ((#1)^32)&,11], ])],{0,1,0}].#&/@clamps[[2]];
clamp3=clamps[[3]];

vnew=Join[clamp1,clamp2,clamp3];

g60withrotatedclamps=Graph[Range[60],UnitEdges[vnew],VertexCoordinates->vnew,
EdgeStyle->Join[
Thread[UnitEdges[clamp1]->Red],
Thread[(UnitEdges[clamp2]/.i_Integer:>i+20)->Green],
Thread[(UnitEdges[clamp3]/.i_Integer:>i+40)->Blue]],VertexStyle->Join[Thread[Range[20]->Red],Thread[Range[21,40]->Green],Thread[Range[41,60]->Blue]],VertexLabels->Automatic,Axes->True,AxesOrigin->{0,0,0},AxesStyle->Directive[Black,Thick],AxesLabel->{"x","y","z"},Ticks->None]

v60=GraphEmbedding[g60withrotatedclamps];

N[v60[[pt]]-v60[[20+pt]],100]

g59=IndexGraph@VertexContract[g60withrotatedclamps,{pt,20+pt}]

VertexCount[g59]

UnitDistanceGraphEmbeddingQ[g59]

EdgeCount[g59]

VertexChromaticNumber[g59]

Point 5

clamps[[1]][[15]]

pt=5;

qx=q/.Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]//RootReduce

N[qx]

clamps[[2]][[15]]

Find the corresponding angle to rotate the y-clamp so that its first point has x == y:

qy=q/.Solve[Equal@@Take[RotationMatrix[q,{0,1,0}].clamps[[2,pt]],2]&&0<q<2π,q]//RootReduce

N[qy]

Manipulate[Show[
Graphics3D[{
Red,Thick,Line[{{0,0,0},RotationMatrix[q1,{1,0,0}].clamps[[1,pt]]}],
Blue,Thickness[.02],Line[{{0,0,0},RotationMatrix[q2,{0,1,0}].clamps[[2,pt]]}]
},PlotRange->1,Axes->True,AxesOrigin->{0,0,0},AxesLabel->{x,y,z},Ticks->None],
ContourPlot3D[x==y,{x,-1,1},{y,-1,1},{z,-1,1}]],
{{q1,N@qx[[1]]},0.,2π},{{q2,N@qy[[1]]},0.,2π}]

clamp1=RotationMatrix[qx[[1]],{1,0,0}].#&/@clamps[[1]];
clamp2=RotationMatrix[qy[[1]],{0,1,0}].#&/@clamps[[2]];
clamp3=clamps[[3]];

vnew=Join[clamp1,clamp2,clamp3];

g60withrotatedclamps=Graph[Range[60],UnitEdges[vnew],VertexCoordinates->vnew,
EdgeStyle->Join[
Thread[UnitEdges[clamp1]->Red],
Thread[(UnitEdges[clamp2]/.i_Integer:>i+20)->Green],
Thread[(UnitEdges[clamp3]/.i_Integer:>i+40)->Blue]],VertexStyle->Join[Thread[Range[20]->Red],Thread[Range[21,40]->Green],Thread[Range[41,60]->Blue]],VertexLabels->Automatic,Axes->True,AxesOrigin->{0,0,0},AxesStyle->Directive[Black,Thick],AxesLabel->{"x","y","z"},Ticks->None]

v60=GraphEmbedding[g60withrotatedclamps];

N[v60[[pt]]-v60[[20+pt]],100]

g59=IndexGraph@VertexContract[g60withrotatedclamps,{pt,20+pt}]

VertexCount[g59]

UnitDistanceGraphEmbeddingQ[g59]

EdgeCount[g59]

VertexChromaticNumber[g59]

Point 6

pt=6;

qx=q/.Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]//RootReduce

N[qx]

Find the corresponding angle to rotate the y-clamp so that its first point has x == y:

qy=q/.Solve[Equal@@Take[RotationMatrix[q,{0,1,0}].clamps[[2,pt]],2]&&0<q<2π,q]//RootReduce

N[qy]

Manipulate[Show[
Graphics3D[{
Red,Thick,Line[{{0,0,0},RotationMatrix[q1,{1,0,0}].clamps[[1,pt]]}],
Blue,Thickness[.02],Line[{{0,0,0},RotationMatrix[q2,{0,1,0}].clamps[[2,pt]]}]
},PlotRange->1,Axes->True,AxesOrigin->{0,0,0},AxesLabel->{x,y,z},Ticks->None],
ContourPlot3D[x==y,{x,-1,1},{y,-1,1},{z,-1,1}]],
{{q1,N@qx[[1]]},0.,2π},{{q2,N@qy[[1]]},0.,2π}]

clamp1=RotationMatrix[qx[[1]],{1,0,0}].#&/@clamps[[1]];
clamp2=RotationMatrix[qy[[1]],{0,1,0}].#&/@clamps[[2]];
clamp3=clamps[[3]];

vnew=Join[clamp1,clamp2,clamp3];

g60withrotatedclamps=Graph[Range[60],UnitEdges[vnew],VertexCoordinates->vnew,
EdgeStyle->Join[
Thread[UnitEdges[clamp1]->Red],
Thread[(UnitEdges[clamp2]/.i_Integer:>i+20)->Green],
Thread[(UnitEdges[clamp3]/.i_Integer:>i+40)->Blue]],VertexStyle->Join[Thread[Range[20]->Red],Thread[Range[21,40]->Green],Thread[Range[41,60]->Blue]],VertexLabels->Automatic,Axes->True,AxesOrigin->{0,0,0},AxesStyle->Directive[Black,Thick],AxesLabel->{"x","y","z"},Ticks->None]

v60=GraphEmbedding[g60withrotatedclamps];

N[v60[[pt]]-v60[[20+pt]],100]

g59=IndexGraph@VertexContract[g60withrotatedclamps,{pt,20+pt}]

VertexCount[g59]

UnitDistanceGraphEmbeddingQ[g59]

EdgeCount[g59]

VertexChromaticNumber[g59]

Point 7 [no solution]

pt=7;

Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]

Point 8 [no solution]

clamps[[1,8]]

However, that cannot be rotated to a position where x == y:

Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,8]],2]&&0<q<2π,q]

Point 9 [no solution]

pt=9;

Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]

Point 10 [no solution]

pt=10;

Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]

Point 11 [no solution]

pt=11;

Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]

Point 12 [no solution]

pt=12;

Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]

Point 13

pt=13;

qx=q/.Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]//RootReduce

N[qx]

Find the corresponding angle to rotate the y-clamp so that its first point has x == y:

qy=q/.Solve[Equal@@Take[RotationMatrix[q,{0,1,0}].clamps[[2,pt]],2]&&0<q<2π,q]//RootReduce

N[qy]

Manipulate[Show[
Graphics3D[{
Red,Thick,Line[{{0,0,0},RotationMatrix[q1,{1,0,0}].clamps[[1,pt]]}],
Blue,Thickness[.02],Line[{{0,0,0},RotationMatrix[q2,{0,1,0}].clamps[[2,pt]]}]
},PlotRange->1,Axes->True,AxesOrigin->{0,0,0},AxesLabel->{x,y,z},Ticks->None],
ContourPlot3D[x==y,{x,-1,1},{y,-1,1},{z,-1,1}]],
{{q1,N@qx[[1]]},0.,2π},{{q2,N@qy[[2]]},0.,2π}]

clamp1=RotationMatrix[qx[[1]],{1,0,0}].#&/@clamps[[1]];
clamp2=RotationMatrix[qy[[2]],{0,1,0}].#&/@clamps[[2]];
clamp3=clamps[[3]];

vnew=Join[clamp1,clamp2,clamp3];

g60withrotatedclamps=Graph[Range[60],UnitEdges[vnew],VertexCoordinates->vnew,
EdgeStyle->Join[
Thread[UnitEdges[clamp1]->Red],
Thread[(UnitEdges[clamp2]/.i_Integer:>i+20)->Green],
Thread[(UnitEdges[clamp3]/.i_Integer:>i+40)->Blue]],VertexStyle->Join[Thread[Range[20]->Red],Thread[Range[21,40]->Green],Thread[Range[41,60]->Blue]],VertexLabels->Automatic,Axes->True,AxesOrigin->{0,0,0},AxesStyle->Directive[Black,Thick],AxesLabel->{"x","y","z"},Ticks->None]

v60=GraphEmbedding[g60withrotatedclamps];

N[v60[[pt]]-v60[[20+pt]],100]

g59=IndexGraph@VertexContract[g60withrotatedclamps,{pt,20+pt}]

VertexCount[g59]

UnitDistanceGraphEmbeddingQ[g59]

EdgeCount[g59]

VertexChromaticNumber[g59]

Point 14

pt=14;

qx=q/.Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]//RootReduce

N[qx]

Find the corresponding angle to rotate the y-clamp so that its first point has x == y:

qy=q/.Solve[Equal@@Take[RotationMatrix[q,{0,1,0}].clamps[[2,pt]],2]&&0<q<2π,q]//RootReduce

N[qy]

Manipulate[Show[
Graphics3D[{
Red,Thick,Line[{{0,0,0},RotationMatrix[q1,{1,0,0}].clamps[[1,pt]]}],
Blue,Thickness[.02],Line[{{0,0,0},RotationMatrix[q2,{0,1,0}].clamps[[2,pt]]}]
},PlotRange->1,Axes->True,AxesOrigin->{0,0,0},AxesLabel->{x,y,z},Ticks->None],
ContourPlot3D[x==y,{x,-1,1},{y,-1,1},{z,-1,1}]],
{{q1,N@qx[[1]]},0.,2π},{{q2,N@qy[[1]]},0.,2π}]

clamp1=RotationMatrix[qx[[1]],{1,0,0}].#&/@clamps[[1]];
clamp2=RotationMatrix[qy[[1]],{0,1,0}].#&/@clamps[[2]];
clamp3=clamps[[3]];

vnew=Join[clamp1,clamp2,clamp3];

g60withrotatedclamps=Graph[Range[60],UnitEdges[vnew],VertexCoordinates->vnew,
EdgeStyle->Join[
Thread[UnitEdges[clamp1]->Red],
Thread[(UnitEdges[clamp2]/.i_Integer:>i+20)->Green],
Thread[(UnitEdges[clamp3]/.i_Integer:>i+40)->Blue]],VertexStyle->Join[Thread[Range[20]->Red],Thread[Range[21,40]->Green],Thread[Range[41,60]->Blue]],VertexLabels->Automatic,Axes->True,AxesOrigin->{0,0,0},AxesStyle->Directive[Black,Thick],AxesLabel->{"x","y","z"},Ticks->None]

v60=GraphEmbedding[g60withrotatedclamps];

N[v60[[pt]]-v60[[20+pt]],100]

g59=IndexGraph@VertexContract[g60withrotatedclamps,{pt,20+pt}]

VertexCount[g59]

UnitDistanceGraphEmbeddingQ[g59]

EdgeCount[g59]

VertexChromaticNumber[g59]

Point 15 [no solution]

pt=15;

Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]

Point 16 [no solution]

pt=16;

Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]

Point 17

pt=17;

qx=q/.Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]//RootReduce

N[qx]

Find the corresponding angle to rotate the y-clamp so that its first point has x == y:

qy=q/.Solve[Equal@@Take[RotationMatrix[q,{0,1,0}].clamps[[2,pt]],2]&&0<q<2π,q]//RootReduce

N[qy]

Manipulate[Show[
Graphics3D[{
Red,Thick,Line[{{0,0,0},RotationMatrix[q1,{1,0,0}].clamps[[1,pt]]}],
Blue,Thickness[.02],Line[{{0,0,0},RotationMatrix[q2,{0,1,0}].clamps[[2,pt]]}]
},PlotRange->1,Axes->True,AxesOrigin->{0,0,0},AxesLabel->{x,y,z},Ticks->None],
ContourPlot3D[x==y,{x,-1,1},{y,-1,1},{z,-1,1}]],
{{q1,N@qx[[1]]},0.,2π},{{q2,N@qy[[2]]},0.,2π}]

clamp1=RotationMatrix[qx[[1]],{1,0,0}].#&/@clamps[[1]];
clamp2=RotationMatrix[qy[[2]],{0,1,0}].#&/@clamps[[2]];
clamp3=clamps[[3]];

vnew=Join[clamp1,clamp2,clamp3];

g60withrotatedclamps=Graph[Range[60],UnitEdges[vnew],VertexCoordinates->vnew,
EdgeStyle->Join[
Thread[UnitEdges[clamp1]->Red],
Thread[(UnitEdges[clamp2]/.i_Integer:>i+20)->Green],
Thread[(UnitEdges[clamp3]/.i_Integer:>i+40)->Blue]],VertexStyle->Join[Thread[Range[20]->Red],Thread[Range[21,40]->Green],Thread[Range[41,60]->Blue]],VertexLabels->Automatic,Axes->True,AxesOrigin->{0,0,0},AxesStyle->Directive[Black,Thick],AxesLabel->{"x","y","z"},Ticks->None]

v60=GraphEmbedding[g60withrotatedclamps];

N[v60[[pt]]-v60[[20+pt]],100]

g59=IndexGraph@VertexContract[g60withrotatedclamps,{pt,20+pt}]

VertexCount[g59]

UnitDistanceGraphEmbeddingQ[g59]

EdgeCount[g59]

VertexChromaticNumber[g59]

Point 18

pt=18;

qx=q/.Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]//RootReduce

N[qx]

Find the corresponding angle to rotate the y-clamp so that its first point has x == y:

qy=q/.Solve[Equal@@Take[RotationMatrix[q,{0,1,0}].clamps[[2,pt]],2]&&0<q<2π,q]//RootReduce

N[qy]

Manipulate[Show[
Graphics3D[{
Red,Thick,Line[{{0,0,0},RotationMatrix[q1,{1,0,0}].clamps[[1,pt]]}],
Blue,Thickness[.02],Line[{{0,0,0},RotationMatrix[q2,{0,1,0}].clamps[[2,pt]]}]
},PlotRange->1,Axes->True,AxesOrigin->{0,0,0},AxesLabel->{x,y,z},Ticks->None],
ContourPlot3D[x==y,{x,-1,1},{y,-1,1},{z,-1,1}]],
{{q1,N@qx[[1]]},0.,2π},{{q2,N@qy[[2]]},0.,2π}]

clamp1=RotationMatrix[qx[[1]],{1,0,0}].#&/@clamps[[1]];
clamp2=RotationMatrix[qy[[2]],{0,1,0}].#&/@clamps[[2]];
clamp3=clamps[[3]];

vnew=Join[clamp1,clamp2,clamp3];

g60withrotatedclamps=Graph[Range[60],UnitEdges[vnew],VertexCoordinates->vnew,
EdgeStyle->Join[
Thread[UnitEdges[clamp1]->Red],
Thread[(UnitEdges[clamp2]/.i_Integer:>i+20)->Green],
Thread[(UnitEdges[clamp3]/.i_Integer:>i+40)->Blue]],VertexStyle->Join[Thread[Range[20]->Red],Thread[Range[21,40]->Green],Thread[Range[41,60]->Blue]],VertexLabels->Automatic,Axes->True,AxesOrigin->{0,0,0},AxesStyle->Directive[Black,Thick],AxesLabel->{"x","y","z"},Ticks->None]

v60=GraphEmbedding[g60withrotatedclamps];

N[v60[[pt]]-v60[[20+pt]],100]

g59=IndexGraph@VertexContract[g60withrotatedclamps,{pt,20+pt}]

VertexCount[g59]

UnitDistanceGraphEmbeddingQ[g59]

EdgeCount[g59]

VertexChromaticNumber[g59]

Point 19 [no solution]

pt=19;

Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]

Point 20 [no solution]

pt=20;

Solve[Equal@@Take[RotationMatrix[q,{1,0,0}].clamps[[1,pt]],2]&&0<q<2π,q]

"DeGreyGraph60"

Construction

de Grey, A. and Haugstrup, A.  "Two small 6-chromatic unit-distance graphs in R."  Geocombinatorics 30, 5–13, 2020.

GraphData[{"Hexahedral",5},"Graph",4]

{x, y, z}, {y, z, x}, {z, x, y} ≈
{±0.0986023, −0.619177, 0.0719291}, {±0.186229, −0.975413, 0.589256},
{±0.258281, −0.918109, −0.406498}, {±0.456858, 0.207921, 0.157792},
{±0.465167, −0.420384, 0.0719291}, {±0.486229, −0.124625, 0.157792},
{±0.5, −1.41798, 0.0119994}, {±0.707107, 0, 0},
{±0.756858, −0.642866, 0.589256}, {±0.777031, −0.553043, −0.406498}

pm[{x_,y_,z_}]:=Sequence@@{{x,y,z},{-x,y,z}}

v=Flatten[{{#,#2,#3},{#2,#3,#},{#3,#,#2}}&@@@{pm@{0.0986023, −0.619177, 0.0719291},pm@{0.186229, −0.975413, 0.589256},
pm@{0.258281, −0.918109, −0.406498}, pm@{0.456858, 0.207921, 0.157792},
pm@{0.465167, −0.420384, 0.0719291}, pm@{.486229, −0.124625, 0.157792},
pm@{1/2, −1.41798, 0.0119994}, pm@{1/Sqrt[2], 0, 0},
pm@{0.756858, −0.642866, 0.589256}, pm@{0.777031, −0.553043, −0.406498}},1]

Length[v]

ee=Select[Subsets[Range[60],{2}],.999<N[EuclideanDistance@@v[[#]]]<1.001&];

Length[ee]

UnitEdges[v]//Length

{Show[g4=Graph[Range@Length@v,ee,VertexCoordinates->v],ViewPoint->10{1,1,1}],}

RecognizeGraph@g4

VertexChromaticNumber[g4,PerformanceGoal->"Quality"]

Abs[EdgeLengths[g4]-1]//Max

g4r=UnitDistanceEmbeddingRefine[g4,PrecisionGoal->1000,WorkingPrecision->2000];//Timing

N[EdgeLengths[g4r]-1,50]//Abs//Max

vexact=Map[ToAlgebraicRoot[N[#,1000]]&,GraphEmbedding[g4r],{2}]

N[vexact-GraphEmbedding[g4r],20]//Abs//Max

g4r2=UnitDistanceEmbeddingRefine[g4r,PrecisionGoal->5000,WorkingPrecision->10000];//Timing

vexact2=Map[ToAlgebraicRoot[N[#,5000]]&,GraphEmbedding[g4r2],{2}]

N[vexact2-GraphEmbedding[g4r2],20]//Abs//Max

vexact2-vexact//Union

g4exact=Graph[Range[60],EdgeList[g4r],VertexCoordinates->vexact2]

Show[g4exact,ViewPoint->10{1,1,1}]

clamps={{{(NumericalApproximation[Root, (RowDefault["0.0986", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,3], ]),(NumericalApproximation[Root, (RowDefault["-0.619", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ])},{(NumericalApproximation[Root, (RowDefault["-0.0986", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.619", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ])},{(NumericalApproximation[Root, (RowDefault["0.186", FEExpressionsNumericalApproximationElider]), Root[-49039671+185779840 #1+398463200 ((#1)^2)+94976000 ((#1)^3)+7840000 ((#1)^4)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.975", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,1], ]),(5/(6 (Sqrt[2])))},{(NumericalApproximation[Root, (RowDefault["-0.186", FEExpressionsNumericalApproximationElider]), Root[-49039671-185779840 #1+398463200 ((#1)^2)-94976000 ((#1)^3)+7840000 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.975", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,1], ]),(5/(6 (Sqrt[2])))},{(NumericalApproximation[Root, (RowDefault["0.258", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,4], ]),(NumericalApproximation[Root, (RowDefault["-0.918", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-0.258", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.918", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ])},{(NumericalApproximation[Root, (RowDefault["0.457", FEExpressionsNumericalApproximationElider]), Root[-71412783+28501280 #1+317218400 ((#1)^2)-85568000 ((#1)^3)+7840000 ((#1)^4)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.208", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,4], ]),(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ])},{(NumericalApproximation[Root, (RowDefault["-0.457", FEExpressionsNumericalApproximationElider]), Root[-71412783-28501280 #1+317218400 ((#1)^2)+85568000 ((#1)^3)+7840000 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.208", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,4], ]),(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ])},{(NumericalApproximation[Root, (RowDefault["0.465", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,3], ]),(NumericalApproximation[Root, (RowDefault["-0.420", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ])},{(NumericalApproximation[Root, (RowDefault["-0.465", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.420", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ])},{(NumericalApproximation[Root, (RowDefault["0.486", FEExpressionsNumericalApproximationElider]), Root[-71412783-28501280 #1+317218400 ((#1)^2)+85568000 ((#1)^3)+7840000 ((#1)^4)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.125", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ])},{(NumericalApproximation[Root, (RowDefault["-0.486", FEExpressionsNumericalApproximationElider]), Root[-71412783+28501280 #1+317218400 ((#1)^2)-85568000 ((#1)^3)+7840000 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.125", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ])},{(1/2),(NumericalApproximation[Root, (RowDefault["-1.42", FEExpressionsNumericalApproximationElider]), Root[-4821911-17325288 ((#1)^2)+9809424 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.0120", FEExpressionsNumericalApproximationElider]), Root[9-62516 ((#1)^2)+68121 ((#1)^4)&,3], ])},{-(1/2),(NumericalApproximation[Root, (RowDefault["-1.42", FEExpressionsNumericalApproximationElider]), Root[-4821911-17325288 ((#1)^2)+9809424 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.0120", FEExpressionsNumericalApproximationElider]), Root[9-62516 ((#1)^2)+68121 ((#1)^4)&,3], ])},{(1/(Sqrt[2])),0,0},{-(1/(Sqrt[2])),0,0},{(NumericalApproximation[Root, (RowDefault["0.757", FEExpressionsNumericalApproximationElider]), Root[-49039671-185779840 #1+398463200 ((#1)^2)-94976000 ((#1)^3)+7840000 ((#1)^4)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.643", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,2], ]),(5/(6 (Sqrt[2])))},{(NumericalApproximation[Root, (RowDefault["-0.757", FEExpressionsNumericalApproximationElider]), Root[-49039671+185779840 #1+398463200 ((#1)^2)+94976000 ((#1)^3)+7840000 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.643", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,2], ]),(5/(6 (Sqrt[2])))},{(NumericalApproximation[Root, (RowDefault["0.777", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,4], ]),(NumericalApproximation[Root, (RowDefault["-0.553", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-0.777", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.553", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ])}},


{{(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ]),(NumericalApproximation[Root, (RowDefault["0.0986", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,3], ]),(NumericalApproximation[Root, (RowDefault["-0.619", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ])},{(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ]),(NumericalApproximation[Root, (RowDefault["-0.0986", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.619", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ])},{(5/(6 (Sqrt[2]))),(NumericalApproximation[Root, (RowDefault["0.186", FEExpressionsNumericalApproximationElider]), Root[-49039671+185779840 #1+398463200 ((#1)^2)+94976000 ((#1)^3)+7840000 ((#1)^4)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.975", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,1], ])},{(5/(6 (Sqrt[2]))),(NumericalApproximation[Root, (RowDefault["-0.186", FEExpressionsNumericalApproximationElider]), Root[-49039671-185779840 #1+398463200 ((#1)^2)-94976000 ((#1)^3)+7840000 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.975", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.258", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,4], ]),(NumericalApproximation[Root, (RowDefault["-0.918", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.258", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.918", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ])},{(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ]),(NumericalApproximation[Root, (RowDefault["0.457", FEExpressionsNumericalApproximationElider]), Root[-71412783+28501280 #1+317218400 ((#1)^2)-85568000 ((#1)^3)+7840000 ((#1)^4)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.208", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,4], ])},{(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ]),(NumericalApproximation[Root, (RowDefault["-0.457", FEExpressionsNumericalApproximationElider]), Root[-71412783-28501280 #1+317218400 ((#1)^2)+85568000 ((#1)^3)+7840000 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.208", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,4], ])},{(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ]),(NumericalApproximation[Root, (RowDefault["0.465", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,3], ]),(NumericalApproximation[Root, (RowDefault["-0.420", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ])},{(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ]),(NumericalApproximation[Root, (RowDefault["-0.465", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.420", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ])},{(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ]),(NumericalApproximation[Root, (RowDefault["0.486", FEExpressionsNumericalApproximationElider]), Root[-71412783-28501280 #1+317218400 ((#1)^2)+85568000 ((#1)^3)+7840000 ((#1)^4)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.125", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,2], ])},{(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ]),(NumericalApproximation[Root, (RowDefault["-0.486", FEExpressionsNumericalApproximationElider]), Root[-71412783+28501280 #1+317218400 ((#1)^2)-85568000 ((#1)^3)+7840000 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.125", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,2], ])},{(NumericalApproximation[Root, (RowDefault["0.0120", FEExpressionsNumericalApproximationElider]), Root[9-62516 ((#1)^2)+68121 ((#1)^4)&,3], ]),(1/2),(NumericalApproximation[Root, (RowDefault["-1.42", FEExpressionsNumericalApproximationElider]), Root[-4821911-17325288 ((#1)^2)+9809424 ((#1)^4)&,1], ])},{(NumericalApproximation[Root, (RowDefault["0.0120", FEExpressionsNumericalApproximationElider]), Root[9-62516 ((#1)^2)+68121 ((#1)^4)&,3], ]),-(1/2),(NumericalApproximation[Root, (RowDefault["-1.42", FEExpressionsNumericalApproximationElider]), Root[-4821911-17325288 ((#1)^2)+9809424 ((#1)^4)&,1], ])},{0,(1/(Sqrt[2])),0},{0,-(1/(Sqrt[2])),0},{(5/(6 (Sqrt[2]))),(NumericalApproximation[Root, (RowDefault["0.757", FEExpressionsNumericalApproximationElider]), Root[-49039671-185779840 #1+398463200 ((#1)^2)-94976000 ((#1)^3)+7840000 ((#1)^4)&,2], ]),(NumericalApproximation[Root, (RowDefault["-0.643", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,2], ])},{(5/(6 (Sqrt[2]))),(NumericalApproximation[Root, (RowDefault["-0.757", FEExpressionsNumericalApproximationElider]), Root[-49039671+185779840 #1+398463200 ((#1)^2)+94976000 ((#1)^3)+7840000 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.643", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,2], ])},{(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.777", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,4], ]),(NumericalApproximation[Root, (RowDefault["-0.553", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.777", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.553", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ])}},

{{(NumericalApproximation[Root, (RowDefault["-0.619", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ]),(NumericalApproximation[Root, (RowDefault["0.0986", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,3], ])},{(NumericalApproximation[Root, (RowDefault["-0.619", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ]),(NumericalApproximation[Root, (RowDefault["-0.0986", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,2], ])},{(NumericalApproximation[Root, (RowDefault["-0.975", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,1], ]),(5/(6 (Sqrt[2]))),(NumericalApproximation[Root, (RowDefault["0.186", FEExpressionsNumericalApproximationElider]), Root[-49039671+185779840 #1+398463200 ((#1)^2)+94976000 ((#1)^3)+7840000 ((#1)^4)&,2], ])},{(NumericalApproximation[Root, (RowDefault["-0.975", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,1], ]),(5/(6 (Sqrt[2]))),(NumericalApproximation[Root, (RowDefault["-0.186", FEExpressionsNumericalApproximationElider]), Root[-49039671-185779840 #1+398463200 ((#1)^2)-94976000 ((#1)^3)+7840000 ((#1)^4)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-0.918", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.258", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,4], ])},{(NumericalApproximation[Root, (RowDefault["-0.918", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337-231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)+813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)-466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)-40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.258", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,1], ])},{(NumericalApproximation[Root, (RowDefault["0.208", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,4], ]),(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ]),(NumericalApproximation[Root, (RowDefault["0.457", FEExpressionsNumericalApproximationElider]), Root[-71412783+28501280 #1+317218400 ((#1)^2)-85568000 ((#1)^3)+7840000 ((#1)^4)&,2], ])},{(NumericalApproximation[Root, (RowDefault["0.208", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,4], ]),(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ]),(NumericalApproximation[Root, (RowDefault["-0.457", FEExpressionsNumericalApproximationElider]), Root[-71412783-28501280 #1+317218400 ((#1)^2)+85568000 ((#1)^3)+7840000 ((#1)^4)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-0.420", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ]),(NumericalApproximation[Root, (RowDefault["0.465", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,3], ])},{(NumericalApproximation[Root, (RowDefault["-0.420", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.0719", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,5], ]),(NumericalApproximation[Root, (RowDefault["-0.465", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,2], ])},{(NumericalApproximation[Root, (RowDefault["-0.125", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ]),(NumericalApproximation[Root, (RowDefault["0.486", FEExpressionsNumericalApproximationElider]), Root[-71412783-28501280 #1+317218400 ((#1)^2)+85568000 ((#1)^3)+7840000 ((#1)^4)&,2], ])},{(NumericalApproximation[Root, (RowDefault["-0.125", FEExpressionsNumericalApproximationElider]), Root[3896110996837908984529-340890593907353873499200 ((#1)^2)+5795166020343840587200000 ((#1)^4)+126316138016984832000000 ((#1)^6)+3521349533721600000000 ((#1)^8)&,2], ]),(NumericalApproximation[Root, (RowDefault["0.158", FEExpressionsNumericalApproximationElider]), Root[2025-93392 ((#1)^2)+484416 ((#1)^4)&,3], ]),(NumericalApproximation[Root, (RowDefault["-0.486", FEExpressionsNumericalApproximationElider]), Root[-71412783+28501280 #1+317218400 ((#1)^2)-85568000 ((#1)^3)+7840000 ((#1)^4)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-1.42", FEExpressionsNumericalApproximationElider]), Root[-4821911-17325288 ((#1)^2)+9809424 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.0120", FEExpressionsNumericalApproximationElider]), Root[9-62516 ((#1)^2)+68121 ((#1)^4)&,3], ]),(1/2)},{(NumericalApproximation[Root, (RowDefault["-1.42", FEExpressionsNumericalApproximationElider]), Root[-4821911-17325288 ((#1)^2)+9809424 ((#1)^4)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.0120", FEExpressionsNumericalApproximationElider]), Root[9-62516 ((#1)^2)+68121 ((#1)^4)&,3], ]),-(1/2)},{0,0,(1/(Sqrt[2]))},{0,0,-(1/(Sqrt[2]))},{(NumericalApproximation[Root, (RowDefault["-0.643", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,2], ]),(5/(6 (Sqrt[2]))),(NumericalApproximation[Root, (RowDefault["0.757", FEExpressionsNumericalApproximationElider]), Root[-49039671-185779840 #1+398463200 ((#1)^2)-94976000 ((#1)^3)+7840000 ((#1)^4)&,2], ])},{(NumericalApproximation[Root, (RowDefault["-0.643", FEExpressionsNumericalApproximationElider]), Root[305487068033032099201-1053520388070000840000 ((#1)^2)+753670321240582080000 ((#1)^4)+16599920198400000000 ((#1)^6)+403275801600000000 ((#1)^8)&,2], ]),(5/(6 (Sqrt[2]))),(NumericalApproximation[Root, (RowDefault["-0.757", FEExpressionsNumericalApproximationElider]), Root[-49039671+185779840 #1+398463200 ((#1)^2)+94976000 ((#1)^3)+7840000 ((#1)^4)&,1], ])},{(NumericalApproximation[Root, (RowDefault["-0.553", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["0.777", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617+1237241351138777994240 #1-1260153795475073894400 ((#1)^2)-11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)-6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)-467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,4], ])},{(NumericalApproximation[Root, (RowDefault["-0.553", FEExpressionsNumericalApproximationElider]), Root[101283246026448098096622636337+231719282073647525003104177920 #1-383488749493421813321061017600 ((#1)^2)-813282260441824456444035072000 ((#1)^3)+276822692791427329837957120000 ((#1)^4)+466524271648835165277388800000 ((#1)^5)+189881906032598461710336000000 ((#1)^6)+40036193999739861073920000000 ((#1)^7)+3692402608671660441600000000 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.406", FEExpressionsNumericalApproximationElider]), Root[37937300625-13329777886208 ((#1)^2)+1404411393212416 ((#1)^4)-48678084047536128 ((#1)^6)+246057649890656256 ((#1)^8)&,1], ]),(NumericalApproximation[Root, (RowDefault["-0.777", FEExpressionsNumericalApproximationElider]), Root[121713695076930223617-1237241351138777994240 #1-1260153795475073894400 ((#1)^2)+11238674046554669056000 ((#1)^3)+17906232318551326720000 ((#1)^4)+6905757532841574400000 ((#1)^5)+2046070267838464000000 ((#1)^6)+467732675952640000000 ((#1)^7)+64451352985600000000 ((#1)^8)&,1], ])}}};

v=Join@@clamps;

UnitEdges[v_,opts___?OptionQ]:=Module[{eps=Lookup[{opts},Tolerance,1*^-6]},UndirectedEdge@@@Select[Subsets[Range[Length[v]],{2}],Abs[EuclideanDistance@@v[[#]]-1]<eps&]//Quiet]

edges=UnitEdges[v]

Length[edges]

Length/@Table[UnitEdges[clamps[[n]]],{n,3}]

Total[%]

g60=Graph[Range[60],edges,VertexCoordinates->v,
EdgeStyle->Join[
Thread[UnitEdges[clamps[[1]]]->Red],
Thread[(UnitEdges[clamps[[2]]]/.i_Integer:>i+20)->Green],
Thread[(UnitEdges[clamps[[3]]]/.i_Integer:>i+40)->Blue]
],
VertexStyle->Join[
Thread[Range[20]->Red],
Thread[Range[21,40]->Green],
Thread[Range[41,60]->Blue]
],
VertexLabels->Automatic,Axes->True,Ticks->None,AxesOrigin->{0,0,0},AxesStyle->Directive[Black,Thick],AxesLabel->{"x","y","z"}]

UnitDistanceGraphEmbeddingQ[g60]

VertexChromaticNumber[g60]

Embeddings

<<MathWorld`Graphs`

Names

GraphData["DeGreyGraph60","StandardName"]

GraphData["DeGreyGraph60","StandardNames"]

Primary

GraphData["DeGreyGraph60"]//StyleGraphs[#,ImageSize->Small]&

All

GraphData["DeGreyGraph60","Graph","All"]//StyleGraphs

Inexact

Select[GraphData["DeGreyGraph60","Graph","All"],(!FreeQ[GraphEmbedding[#],_?InexactNumberQ]&)]//StyleGraphs

Embedding types

GraphDataEmbeddings[GraphData["DeGreyGraph60","EdgeList"]]

Default embedding

GraphPlot@GraphData["DeGreyGraph60","Edges"]

g=Graph[GraphData["DeGreyGraph60","Edges"],GraphLayout->"SpringEmbedding"]

GraphPlot[GraphData["DeGreyGraph60","Edges"],GraphLayout->"HighDimensionalEmbedding"]

v={};
g=Graph[Range[Length[v]],UndirectedEdge@@@{},VertexCoordinates->v,VertexLabels->Automatic]

RecognizeGraph[g]

Degenerate

GraphData["DeGreyGraph60","Graph","Degenerate"]//StyleGraphs

DegenerateGraphEmbeddingTypes/@GraphData["DeGreyGraph60","Graph","Degenerate"]

Bilateral

GraphData["DeGreyGraph60","Graph","Bilateral"]//StyleGraphs

Circular

GraphData["DeGreyGraph60","Graph","Circular"]//StyleGraphs

Circular construction

FindHamiltonianCycle[GraphData["DeGreyGraph60"]]//Timing

Length[hc=FindHamiltonianCycle[GraphData["DeGreyGraph60"],All][[All,All,1]]]

Length[bilat=DeleteDuplicatesBy[
DeleteMissing[BilaterallyRotatedGraph@CircularEmbeddingFromHamiltonianCycle[GraphData["DeGreyGraph60"],#]&/@hc],
CircularCanonicalGraphEmbedding]]//Timing

gs=bilat

Length[quad=DeleteDuplicatesBy[Union@Select[bilat,BilateralGraphEmbeddingQ[#,Axis->"X"]&],CircularCanonicalGraphEmbedding[#,4]&]]

quad

Planar

GraphData["DeGreyGraph60","Planar"]

GraphData["DeGreyGraph60","Graph","Planar"]//StyleGraphs

MinimalCrossing

GraphData["DeGreyGraph60",{"RCN","CN"}]

GraphData["DeGreyGraph60","Graph","MinimalCrossing"]//StyleGraphs

MinimalCrossing construction

(cn=CrossingNumber[GraphData["DeGreyGraph60"],TimeConstraint->1])//AbsoluteTiming

(cn=CrossingNumber[GraphData["DeGreyGraph60"],TimeConstraint->10])//AbsoluteTiming

(cn=CrossingNumber[GraphData["DeGreyGraph60"],TimeConstraint->60])//AbsoluteTiming

Union[Select[Table[RotateGraph[MinimalCrossingGraph[GraphData["DeGreyGraph60"],"CrossingNumber"->cn,RandomSeed->n]],{n,50}],Max[OuterFace[#]]<=GraphData["DeGreyGraph60","V"]&]]//Timing

Table[MinimalCrossingGraph[GraphData["DeGreyGraph60"],"CrossingNumber"->cn,RandomSeed->i],{i,50}]//Union

GraphPlot@RotateGraph[,-4Pi/7,VertexSize->Scaled[.02]]

v={};
g=Graph[Range[Length[v]],UndirectedEdge@@@{},VertexCoordinates->v,VertexLabels->Automatic]

RecognizeGraph[g]

RectilinearCrossingCount[g]

Circulant

GraphData["DeGreyGraph60","Circulant"]

GraphData["DeGreyGraph60","Graph","Circulant"]//StyleGraphs

Line graph

GraphData["DeGreyGraph60","Line"]

LineGraphQ[GraphData["DeGreyGraph60"]]//Timing

RootGraph

Select[GraphData[All],GraphData[#,"LineGraph","Name"]=== "DeGreyGraph60"&]

RootGraph[GraphData["DeGreyGraph60"]]

Halin

GraphData["DeGreyGraph60","Halin"]

GraphData["DeGreyGraph60","Graph","Halin"]//StyleGraphs

Rigid

GraphData["DeGreyGraph60","Rigid"]

GraphData["DeGreyGraph60","Graph","Rigid"]//StyleGraphs

Flexible

GraphData["DeGreyGraph60","Flexible"]

GraphData["DeGreyGraph60","Graph","Flexible"]//StyleGraphs

LCF

GraphData["DeGreyGraph60","LCF"]

GraphData["DeGreyGraph60","HamiltonianCycleCount"]

GraphData["DeGreyGraph60","LCFSignature"]

GraphData["DeGreyGraph60","LCFNotations"]

GraphData["DeGreyGraph60","Graph","LCF"]//StyleGraphs

Tally[LCFNotation[#][[2]]&/@%]

UnitDistance

GraphData["DeGreyGraph60","UnitDistance"]

UnitDistanceGraphQ[GraphData["DeGreyGraph60"],Debug->True]//Timing

GraphData["DeGreyGraph60","Graph","UnitDistance"]//StyleGraphs

Select[%,!FreeQ[GraphEmbedding[#],_?InexactNumberQ]&]

UnitDistance by refinement

UnitDistanceEmbeddingRefine[Graph[GraphData["DeGreyGraph60","VertexList"],GraphData["DeGreyGraph60","EdgeList"]],MaxIterations->500]

UnitDistanceEmbeddingRefine[Annotate[#,VertexCoordinates->N[GraphEmbedding[#]]],MaxIterations->500]&/@Complement@@(GraphData["DeGreyGraph60","Graph",#]&/@{"All","UnitDistance"})

UnitDistance by FindUnitDistanceEmbedding

FindUnitDistanceEmbedding[GraphData["DeGreyGraph60"],MaxIterations->5000,"ReturnWithMessage"->True]//Timing

Matchstick

GraphData["DeGreyGraph60","Matchstick"]

GraphData["DeGreyGraph60","Graph","Matchstick"]//StyleGraphs

3D default

Graph3D[GraphData["DeGreyGraph60","Edges"]]

3D All

GraphData["DeGreyGraph60","Graph",{"3D","All"}]

3D UnitDistance

GraphData["DeGreyGraph60","Graph",{"3D","UnitDistance"}]

3D Polyhedron

GraphData["DeGreyGraph60","Polyhedral"]

GraphData["DeGreyGraph60","Graph",{"3D","Polyhedron"}]

"DeGreyGraph126"

GraphData["DeGreyGraph126"]

Construction

Parts, J.  "A Small 6-Chromatic Two-Distance Graph in the Plane."  23 Oct 2020.  https://arxiv.org/abs/2010.12656

https://arxiv.org/pdf/2010.12656.pdf

First[2/.Import["https://arxiv.org/pdf/2010.12656.pdf","EmbeddedImages"]]

Corresponding graph was defined explicitly by de Grey [3]:

[3] A. de Grey, Comments in Polymath16 , thread 14, comment 24439, October 20, 2019

https://dustingmixon.wordpress.com/2019/08/05/polymath16-fourteenth-thread-automated-graph-minimization/#comment-24439

G126 =G5 ⊕G5 ⊕G5 ⊕G5 ⊕G5,

Here G5 is a regular pentagon with side 1 and diagonal d =((Sqrt[5])+1)/2, and ⊕ denotes the Minkowski sum. The Minkowski sum of distance graphs is a graph whose vertex set is the union of all possible sums of their vertex coordinates, and the set of edges includes all pairs of obtained vertices for all forbidden distances.The size of this graph is much smaller than we expected – it has only 126 vertices, and 350 edges each of length 1 and d (Fig. 1).

Vertex coordinates

SetDirectory["/Users/eww/Documents/Mathematica/Paclets/GraphData/Collections/UnitDistance/Parts/126"];

Length[v=ToExpression/@Import["g126.vtx","Lines"]]

Length[e=Select[Subsets[Range[Length[v]],{2}],Abs[(d=EuclideanDistance@@v[[#]])-1]<.001||Abs[d-GoldenRatio]<.001&]]//Quiet//Timing

(G126=Graph[Range[Length[v]],UndirectedEdge@@@e,VertexCoordinates->v])

EdgeLengths[G126]//RootReduce//Tally

RecognizeGraph[G126]

GraphData["PartsGraph16"]

FindIsomorphicSubgraph[G126,GraphData["PartsGraph16"]]//Timing

VertexChromaticNumber[G126]//Timing

GraphData

file=OpenWrite["~/degrey.m"]

WriteString[file,GraphDataString[G126,
"StandardName"->"DeGreyGraph126",
"Name"->"de Grey graph 126",
"ChromaticNumber"->5,
"Skip"->{"CliqueCoveringNumber","ConnectedInducedSubgraphPolynomial","CrossingNumber","DominatingSet","GracefulLabeling","GracefulLabelings","IndependencePolynomial","MatchingGeneratingPolynomial","MatchingPolynomial","RadioNumber","TotalDominatingSet","VertexCover"},
TimeConstraint->5,
Debug->True]]

Close[file]

"DeGreyGraph"

GraphData["DeGreyGraph","StandardName"]

GraphData["DeGreyGraph","StandardNames"]

ColorGraph[g_Graph]:=Module[{col=FindVertexColoring[g],cols={Red,Green,Yellow,Green,Blue}},
Annotate[g,{EdgeStyle->Directive[LightGray],VertexStyle->MapIndexed[#2[[1]]->cols[[#]]&,col]}]
]

g=ColorGraph[GraphData["DeGreyGraph"]]

GraphData[gname,{"V","M"}]

UnitDistanceGraphQ[g,WorkingPrecision->∞]//FullSimplify//Timing

VertexChromaticNumber[g]//Timing

Construct

https://gilkalai.wordpress.com/2018/04/10/aubrey-de-grey-the-chromatic-number-of-the-plane-is-at-least-5/#comment-40108

SetDirectory["/Users/eww/Documents/Mathematica/Paclets/GraphData/Collections/Hadwiger-Nelson/1581"]

FileNames[]

Length[v=ToExpression/@Import["1581v.txt","Lines"]]

Length[e=ToExpression/@Import["1581e.txt","Lines"]]

(deGreyGraph=System`Graph[Range[Length[v]],UndirectedEdge@@@e,VertexCoordinates->v])

Compute Properties

TriangleFreeGraphQ[deGreyGraph]

UnitDistanceGraphQ[deGreyGraph]

UnitDistanceGraphQ[deGreyGraph,WorkingPrecision->∞]//FullSimplify//Timing

FindVertexColoring[deGreyGraph,Method->"Brelaz"]//Max//Timing

FindVertexColoring[deGreyGraph,Method->"Combinatorica"]//Max//Timing

FindVertexColoring[deGreyGraph,Method->{"ILP",3}]//Max//Timing

GraphData

GraphDataString

file=OpenWrite["~/degrey.m"]

g=;

WriteString[file,GraphDataString[g,
"StandardName"->"DeGreyGraph60",
"Name"->"de Grey graph 60",
"Skip"->{"Anarboricity","Arboricity","BroadcastTime","BroadcastTimes","ChromaticPolynomial","ConstructionNumber","ConnectedInducedSubgraphPolynomial","Cycles","CyclicEdgeConnectivity","EdgeChromaticNumber","Hamiltonian","HamiltonianCycleCount","HamiltonianCycle","HamiltonianCycles","HamiltonianPaths","HamiltonianWalks","IdiosyncraticPolynomial","IrredundacePolynomial","LinklesslyEmbeddable","LongestCycle","LowerIndependenceNumber","LowerMatchingNumber","MatchingGeneratingPolynomial","MaximalIndependentEdgeSets","MaximumIndependentEdgeSetCount","MaximumIndependentEdgeSets","MetricDimension","MinimumEdgeColoring","MinimumWeightFractionalEdgeColoring","MinimumWeightFractionalColoring","Minors","MinimumCyclicEdgeCut","MinimumCyclicEdgeCutCount","MinimumCyclicEdgeCuts","Pancyclic","PathPolynomial","ProjectivePlanar","QuadraticEmbeddingConstant","TuttePolynomial","UniquelyHamiltonian"},
TimeConstraint->10,
Debug->True]]

Close[file]