Truncated Pentakis Dodecahedron

Author

Eric W. Weisstein
August 16, 2022

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Polyhedra/TruncatedPentakisDodecahedron.nb.

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

©2022 Wolfram Research, Inc. except for portions noted otherwise

Sources

Wikipedia

https://en.wikipedia.org/wiki/Truncated_pentakis_dodecahedron

Coeey

http://dmccooey.com/polyhedra/TruncatedPentakisDodecahedron1.html

Figure

GraphicsRow[{Graphics3D[{Opacity[.8],PolyhedronData["TruncatedPentakisDodecahedron","Polyhedron"]},Boxed->False],
Show[,ImageSize->Automatic],Graphics3D[{Opacity[.5],Red,PolyhedronData["TruncatedPentakisDodecahedron","Polyhedron"],Yellow,PolyhedronData["TruncatedPentakisDodecahedron","Midsphere"]},Boxed->False]}]

Solid

PolyhedronData["TruncatedPentakisDodecahedron","Orientations"]

PolyhedronData["TruncatedPentakisDodecahedron"]

Graphics3D[{FaceForm[Green,Red],PolyhedronData["TruncatedPentakisDodecahedron","Polyhedron"]}]

PolyhedronData["TruncatedPentakisDodecahedron","Region"]

Solid and Dual

PolyhedronData["TruncatedPentakisDodecahedron","Dual"]

PolyhedronData["TruncatedPentakisDodecahedron",#]&/@{"Graphics3D","Dual","DualCompound"}

Net

Quit

PolyhedronData["TruncatedPentakisDodecahedron","Net"]

PolyhedronData["TruncatedPentakisDodecahedron","Net","Colored"]

NetPrintout[PolyhedronData["TruncatedPentakisDodecahedron","Polyhedron"],"TruncatedPentakisDodecahedron.pdf"]

Properties

p=PolyhedronData[pname="TruncatedPentakisDodecahedron","Polyhedron"]

Centroid

Graphics3D[{AbsolutePointSize[10],
Point[{0,0,0}],{Blue,Point[PolyhedronData[pname,"Centroid"]]},Opacity[.2],PolyhedronData[pname,"GraphicsComplex"]}]

PolyhedronData[pname,"Centroid"]

RegionCentroid[p]//RootReduce//Quiet//Timing

PolyhedronCentroid[p]//Quiet//Timing

Circumsphere

sphere=PolyhedronData[pname,"Circumsphere"]

sphere=Circumsphere[p]

(sphere=MyCircumsphere[p])//Timing

Compound

PolyhedronData[pname,"Compound"]

Convex

PolyhedronData[pname,"Convex"]

ConvexPolyhedronQ[p]

DihedralAngles

PolyhedronData[pname,"DihedralAngles"]//Tally

SimplifyNumericallyDistinct[DihedralAngles[p]]//Tally

EdgeCount

PolyhedronData[pname,"EdgeCount"]

EdgeLengths

PolyhedronData[pname,"EdgeLengths"]

SortBy[SimplifyNumericallyDistinct[PolyhedronData[pname,"Lines"]/.Line[l_]:>EuclideanDistance@@l]//Union,N]//Quiet

ByteCount/@{(NumericalApproximation[Root, (RowDefault["1.07", FEExpressionsNumericalApproximationElider]), Root[9-9 ((#1)^2)+((#1)^4)&,3], ]),(Sqrt[(6/(3+(Sqrt[5])))])}

lens=SimplifyNumericallyDistinct[PolyhedronEdgeLengths[p]];//Quiet

(distinctlens=Mean/@Split[Sort[lens],Abs[#1-#2]<1.*^-10&])//N//Quiet

v=PolyhedronCoordinates[p];

colors=With[{n=Length[distinctlens]},Table[Hue[i/n],{i,0,n-1}]]

Graphics3D[{Thick,Sequence@@Nearest[Thread[distinctlens->colors],EuclideanDistance@@v[[#]]],Line[v[[#]]]}&/@PolyhedronEdges[p],Boxed->False]//Quiet

FaceCount

PolyhedronData[pname,"FaceCount"]

Faces

GeneralizedDiameter

PolyhedronData[pname,"GeneralizedDiameter"]

GeneralizedDiameter[p]//FullSimplify//Quiet

InertiaTensor

PolyhedronData[pname,"InertiaTensor"]

(i=((MomentOfInertia[p,{0,0,0}])/(Volume[p])))//Timing

N[i]//Chop

Map[ToAlgebraicRoot,i,{2}]//FullSimplify//Quiet

PolyhedronInertiaTensor[p]//Timing

Insphere

PolyhedronData[pname,"Insphere"]

Insphere[p]//Timing

MyInsphere[p]//Timing

MeanCylindricalRadius

((NIntegrate[(Sqrt[(x^2)+(y^2)]),{x,y,z}∈p])/vol)//Timing

(i=((Integrate[(Sqrt[(x^2)+(y^2)]),{x,y,z}∈p])/vol))//Timing

N[i]

MeanSquareCylindricalRadius

((NIntegrate[(x^2)+(y^2),{x,y,z}∈p])/vol)//Timing

(i=((Integrate[(x^2)+(y^2),{x,y,z}∈p])/vol)//FullSimplify)//Timing

N[i]

MeanSphericalRadius

((NIntegrate[(Sqrt[(x^2)+(y^2)+(z^2)]),{x,y,z}∈p])/vol)//Timing

(i=((Integrate[(Sqrt[(x^2)+(y^2)+(z^2)]),{x,y,z}∈p])/(PolyhedronData[pname,"Volume"])))//Timing

N[i]

MeanSquareSphericalRadius

((NIntegrate[(x^2)+(y^2)+(z^2),{x,y,z}∈p])/vol)//Timing

(i=((Integrate[(x^2)+(y^2)+(z^2),{x,y,z}∈p])/vol)//FullSimplify)//Timing

N[i]

Midsphere

sphere=PolyhedronData[pname,"Midsphere"]

(sphere=Midsphere[p])//Timing

(sphere=Midsphere[p,Method->"PointLineDistance"])//FullSimplify//Timing

Graphics3D[{{Opacity[.5],Yellow,p},{Red,sphere}},Boxed->False]

Region

PolyhedronData[pname,"Region"]

RegionFunction

Collect[#,{x,y,z},RootReduce]&/@PolyhedronInequalities[p,{x,y,z}]

reg=(1/4) (-2-7 (Sqrt[5]))+(x/2)+(1/4) (1+(Sqrt[5])) z≤0&&(1/4) (-2-7 (Sqrt[5]))+(x/2)+(1/4) (-1-(Sqrt[5])) z≤0&&(1/4) (-2-7 (Sqrt[5]))-(x/2)+(1/4) (1+(Sqrt[5])) z≤0&&(1/4) (-2-7 (Sqrt[5]))-(x/2)+(1/4) (-1-(Sqrt[5])) z≤0&&(1/4) (-2-7 (Sqrt[5]))+(1/4) (1+(Sqrt[5])) x+(y/2)≤0&&(1/4) (-2-7 (Sqrt[5]))+(1/4) (1+(Sqrt[5])) x-(y/2)≤0&&(1/4) (-2-7 (Sqrt[5]))+(1/4) (-1-(Sqrt[5])) x+(y/2)≤0&&(1/4) (-2-7 (Sqrt[5]))+(1/4) (-1-(Sqrt[5])) x-(y/2)≤0&&(1/4) (-2-7 (Sqrt[5]))+(1/4) (1+(Sqrt[5])) y+(z/2)≤0&&(1/4) (-2-7 (Sqrt[5]))+(1/4) (1+(Sqrt[5])) y-(z/2)≤0&&(1/4) (-2-7 (Sqrt[5]))+(1/4) (-1-(Sqrt[5])) y+(z/2)≤0&&(1/4) (-2-7 (Sqrt[5]))+(1/4) (-1-(Sqrt[5])) y-(z/2)≤0&&z (NumericalApproximation[Root, (RowDefault["1.13", FEExpressionsNumericalApproximationElider]), Root[106929-79344 #1-13560 ((#1)^2)-192 ((#1)^3)+16 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["0.232", FEExpressionsNumericalApproximationElider]), Root[11881-45024 #1-26820 ((#1)^2)+1728 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&z (NumericalApproximation[Root, (RowDefault["1.05", FEExpressionsNumericalApproximationElider]), Root[11881-10076 #1-1348 ((#1)^2)+176 ((#1)^3)+16 ((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["0.402", FEExpressionsNumericalApproximationElider]), Root[11881-32404 #1+6812 ((#1)^2)+784 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&z (NumericalApproximation[Root, (RowDefault["-1.13", FEExpressionsNumericalApproximationElider]), Root[106929+79344 #1-13560 ((#1)^2)+192 ((#1)^3)+16 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.232", FEExpressionsNumericalApproximationElider]), Root[11881+45024 #1-26820 ((#1)^2)-1728 ((#1)^3)+144 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&z (NumericalApproximation[Root, (RowDefault["-1.05", FEExpressionsNumericalApproximationElider]), Root[11881+10076 #1-1348 ((#1)^2)-176 ((#1)^3)+16 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["0.402", FEExpressionsNumericalApproximationElider]), Root[11881-32404 #1+6812 ((#1)^2)+784 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&z (NumericalApproximation[Root, (RowDefault["1.13", FEExpressionsNumericalApproximationElider]), Root[106929-79344 #1-13560 ((#1)^2)-192 ((#1)^3)+16 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["-0.232", FEExpressionsNumericalApproximationElider]), Root[11881+45024 #1-26820 ((#1)^2)-1728 ((#1)^3)+144 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.402", FEExpressionsNumericalApproximationElider]), Root[11881+32404 #1+6812 ((#1)^2)-784 ((#1)^3)+16 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["1.05", FEExpressionsNumericalApproximationElider]), Root[11881-10076 #1-1348 ((#1)^2)+176 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&z (NumericalApproximation[Root, (RowDefault["-1.13", FEExpressionsNumericalApproximationElider]), Root[106929+79344 #1-13560 ((#1)^2)+192 ((#1)^3)+16 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["0.232", FEExpressionsNumericalApproximationElider]), Root[11881-45024 #1-26820 ((#1)^2)+1728 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.402", FEExpressionsNumericalApproximationElider]), Root[11881+32404 #1+6812 ((#1)^2)-784 ((#1)^3)+16 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-1.05", FEExpressionsNumericalApproximationElider]), Root[11881+10076 #1-1348 ((#1)^2)-176 ((#1)^3)+16 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&x (NumericalApproximation[Root, (RowDefault["1.13", FEExpressionsNumericalApproximationElider]), Root[106929-79344 #1-13560 ((#1)^2)-192 ((#1)^3)+16 ((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["0.232", FEExpressionsNumericalApproximationElider]), Root[11881-45024 #1-26820 ((#1)^2)+1728 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["1.05", FEExpressionsNumericalApproximationElider]), Root[11881-10076 #1-1348 ((#1)^2)+176 ((#1)^3)+16 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.402", FEExpressionsNumericalApproximationElider]), Root[11881-32404 #1+6812 ((#1)^2)+784 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&x (NumericalApproximation[Root, (RowDefault["1.13", FEExpressionsNumericalApproximationElider]), Root[106929-79344 #1-13560 ((#1)^2)-192 ((#1)^3)+16 ((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["-0.232", FEExpressionsNumericalApproximationElider]), Root[11881+45024 #1-26820 ((#1)^2)-1728 ((#1)^3)+144 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&z (NumericalApproximation[Root, (RowDefault["-0.402", FEExpressionsNumericalApproximationElider]), Root[11881+32404 #1+6812 ((#1)^2)-784 ((#1)^3)+16 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["1.05", FEExpressionsNumericalApproximationElider]), Root[11881-10076 #1-1348 ((#1)^2)+176 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-1.13", FEExpressionsNumericalApproximationElider]), Root[106929+79344 #1-13560 ((#1)^2)+192 ((#1)^3)+16 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["-0.232", FEExpressionsNumericalApproximationElider]), Root[11881+45024 #1-26820 ((#1)^2)-1728 ((#1)^3)+144 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-1.05", FEExpressionsNumericalApproximationElider]), Root[11881+10076 #1-1348 ((#1)^2)-176 ((#1)^3)+16 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["0.402", FEExpressionsNumericalApproximationElider]), Root[11881-32404 #1+6812 ((#1)^2)+784 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-1.13", FEExpressionsNumericalApproximationElider]), Root[106929+79344 #1-13560 ((#1)^2)+192 ((#1)^3)+16 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["0.232", FEExpressionsNumericalApproximationElider]), Root[11881-45024 #1-26820 ((#1)^2)+1728 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&z (NumericalApproximation[Root, (RowDefault["-0.402", FEExpressionsNumericalApproximationElider]), Root[11881+32404 #1+6812 ((#1)^2)-784 ((#1)^3)+16 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-1.05", FEExpressionsNumericalApproximationElider]), Root[11881+10076 #1-1348 ((#1)^2)-176 ((#1)^3)+16 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&y (NumericalApproximation[Root, (RowDefault["1.13", FEExpressionsNumericalApproximationElider]), Root[106929-79344 #1-13560 ((#1)^2)-192 ((#1)^3)+16 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.232", FEExpressionsNumericalApproximationElider]), Root[11881-45024 #1-26820 ((#1)^2)+1728 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&y (NumericalApproximation[Root, (RowDefault["1.05", FEExpressionsNumericalApproximationElider]), Root[11881-10076 #1-1348 ((#1)^2)+176 ((#1)^3)+16 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["0.402", FEExpressionsNumericalApproximationElider]), Root[11881-32404 #1+6812 ((#1)^2)+784 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-1.13", FEExpressionsNumericalApproximationElider]), Root[106929+79344 #1-13560 ((#1)^2)+192 ((#1)^3)+16 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.232", FEExpressionsNumericalApproximationElider]), Root[11881+45024 #1-26820 ((#1)^2)-1728 ((#1)^3)+144 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-1.05", FEExpressionsNumericalApproximationElider]), Root[11881+10076 #1-1348 ((#1)^2)-176 ((#1)^3)+16 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["0.402", FEExpressionsNumericalApproximationElider]), Root[11881-32404 #1+6812 ((#1)^2)+784 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&y (NumericalApproximation[Root, (RowDefault["1.13", FEExpressionsNumericalApproximationElider]), Root[106929-79344 #1-13560 ((#1)^2)-192 ((#1)^3)+16 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["-0.232", FEExpressionsNumericalApproximationElider]), Root[11881+45024 #1-26820 ((#1)^2)-1728 ((#1)^3)+144 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-0.402", FEExpressionsNumericalApproximationElider]), Root[11881+32404 #1+6812 ((#1)^2)-784 ((#1)^3)+16 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["1.05", FEExpressionsNumericalApproximationElider]), Root[11881-10076 #1-1348 ((#1)^2)+176 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-1.13", FEExpressionsNumericalApproximationElider]), Root[106929+79344 #1-13560 ((#1)^2)+192 ((#1)^3)+16 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["0.232", FEExpressionsNumericalApproximationElider]), Root[11881-45024 #1-26820 ((#1)^2)+1728 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-0.402", FEExpressionsNumericalApproximationElider]), Root[11881+32404 #1+6812 ((#1)^2)-784 ((#1)^3)+16 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["-1.05", FEExpressionsNumericalApproximationElider]), Root[11881+10076 #1-1348 ((#1)^2)-176 ((#1)^3)+16 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&(y/(2 (Sqrt[3])))+x (NumericalApproximation[Root, (RowDefault["0.357", FEExpressionsNumericalApproximationElider]), Root[1-9 ((#1)^2)+9 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.756", FEExpressionsNumericalApproximationElider]), Root[1-84 ((#1)^2)+144 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-4.06", FEExpressionsNumericalApproximationElider]), Root[106929-10704 ((#1)^2)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["0.464", FEExpressionsNumericalApproximationElider]), Root[11881-22512 #1-6705 ((#1)^2)+216 ((#1)^3)+9 ((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["0.376", FEExpressionsNumericalApproximationElider]), Root[11881-26448 #1-13560 ((#1)^2)-576 ((#1)^3)+144 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["-0.984", FEExpressionsNumericalApproximationElider]), Root[11881+7872 #1-4980 ((#1)^2)-576 ((#1)^3)+144 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["0.464", FEExpressionsNumericalApproximationElider]), Root[11881-22512 #1-6705 ((#1)^2)+216 ((#1)^3)+9 ((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["-0.376", FEExpressionsNumericalApproximationElider]), Root[11881+26448 #1-13560 ((#1)^2)+576 ((#1)^3)+144 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["0.984", FEExpressionsNumericalApproximationElider]), Root[11881-7872 #1-4980 ((#1)^2)+576 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&-(y/(2 (Sqrt[3])))+x (NumericalApproximation[Root, (RowDefault["0.357", FEExpressionsNumericalApproximationElider]), Root[1-9 ((#1)^2)+9 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["-0.756", FEExpressionsNumericalApproximationElider]), Root[1-84 ((#1)^2)+144 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-4.06", FEExpressionsNumericalApproximationElider]), Root[106929-10704 ((#1)^2)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-0.464", FEExpressionsNumericalApproximationElider]), Root[11881+22512 #1-6705 ((#1)^2)-216 ((#1)^3)+9 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["0.376", FEExpressionsNumericalApproximationElider]), Root[11881-26448 #1-13560 ((#1)^2)-576 ((#1)^3)+144 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.984", FEExpressionsNumericalApproximationElider]), Root[11881-7872 #1-4980 ((#1)^2)+576 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&(y/(2 (Sqrt[3])))+x (NumericalApproximation[Root, (RowDefault["-0.357", FEExpressionsNumericalApproximationElider]), Root[1-9 ((#1)^2)+9 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.756", FEExpressionsNumericalApproximationElider]), Root[1-84 ((#1)^2)+144 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-4.06", FEExpressionsNumericalApproximationElider]), Root[106929-10704 ((#1)^2)+256 ((#1)^4)&,2], ])≤0&&-(y/(2 (Sqrt[3])))+x (NumericalApproximation[Root, (RowDefault["-0.357", FEExpressionsNumericalApproximationElider]), Root[1-9 ((#1)^2)+9 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["0.756", FEExpressionsNumericalApproximationElider]), Root[1-84 ((#1)^2)+144 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-4.06", FEExpressionsNumericalApproximationElider]), Root[106929-10704 ((#1)^2)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-0.464", FEExpressionsNumericalApproximationElider]), Root[11881+22512 #1-6705 ((#1)^2)-216 ((#1)^3)+9 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.984", FEExpressionsNumericalApproximationElider]), Root[11881+7872 #1-4980 ((#1)^2)-576 ((#1)^3)+144 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["-0.376", FEExpressionsNumericalApproximationElider]), Root[11881+26448 #1-13560 ((#1)^2)+576 ((#1)^3)+144 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&(z/(2 (Sqrt[3])))+y (NumericalApproximation[Root, (RowDefault["0.357", FEExpressionsNumericalApproximationElider]), Root[1-9 ((#1)^2)+9 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["0.756", FEExpressionsNumericalApproximationElider]), Root[1-84 ((#1)^2)+144 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-4.06", FEExpressionsNumericalApproximationElider]), Root[106929-10704 ((#1)^2)+256 ((#1)^4)&,2], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.464", FEExpressionsNumericalApproximationElider]), Root[11881-22512 #1-6705 ((#1)^2)+216 ((#1)^3)+9 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["-0.376", FEExpressionsNumericalApproximationElider]), Root[11881+26448 #1-13560 ((#1)^2)+576 ((#1)^3)+144 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["0.984", FEExpressionsNumericalApproximationElider]), Root[11881-7872 #1-4980 ((#1)^2)+576 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.464", FEExpressionsNumericalApproximationElider]), Root[11881+22512 #1-6705 ((#1)^2)-216 ((#1)^3)+9 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["0.376", FEExpressionsNumericalApproximationElider]), Root[11881-26448 #1-13560 ((#1)^2)-576 ((#1)^3)+144 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["0.984", FEExpressionsNumericalApproximationElider]), Root[11881-7872 #1-4980 ((#1)^2)+576 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&-(z/(2 (Sqrt[3])))+y (NumericalApproximation[Root, (RowDefault["-0.357", FEExpressionsNumericalApproximationElider]), Root[1-9 ((#1)^2)+9 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["0.756", FEExpressionsNumericalApproximationElider]), Root[1-84 ((#1)^2)+144 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-4.06", FEExpressionsNumericalApproximationElider]), Root[106929-10704 ((#1)^2)+256 ((#1)^4)&,2], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.464", FEExpressionsNumericalApproximationElider]), Root[11881-22512 #1-6705 ((#1)^2)+216 ((#1)^3)+9 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.376", FEExpressionsNumericalApproximationElider]), Root[11881-26448 #1-13560 ((#1)^2)-576 ((#1)^3)+144 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["-0.984", FEExpressionsNumericalApproximationElider]), Root[11881+7872 #1-4980 ((#1)^2)-576 ((#1)^3)+144 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&-(z/(2 (Sqrt[3])))+y (NumericalApproximation[Root, (RowDefault["0.357", FEExpressionsNumericalApproximationElider]), Root[1-9 ((#1)^2)+9 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["-0.756", FEExpressionsNumericalApproximationElider]), Root[1-84 ((#1)^2)+144 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-4.06", FEExpressionsNumericalApproximationElider]), Root[106929-10704 ((#1)^2)+256 ((#1)^4)&,2], ])≤0&&(z/(2 (Sqrt[3])))+y (NumericalApproximation[Root, (RowDefault["-0.357", FEExpressionsNumericalApproximationElider]), Root[1-9 ((#1)^2)+9 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.756", FEExpressionsNumericalApproximationElider]), Root[1-84 ((#1)^2)+144 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-4.06", FEExpressionsNumericalApproximationElider]), Root[106929-10704 ((#1)^2)+256 ((#1)^4)&,2], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.464", FEExpressionsNumericalApproximationElider]), Root[11881+22512 #1-6705 ((#1)^2)-216 ((#1)^3)+9 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.984", FEExpressionsNumericalApproximationElider]), Root[11881+7872 #1-4980 ((#1)^2)-576 ((#1)^3)+144 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.376", FEExpressionsNumericalApproximationElider]), Root[11881+26448 #1-13560 ((#1)^2)+576 ((#1)^3)+144 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&(x/(2 (Sqrt[3])))+z (NumericalApproximation[Root, (RowDefault["0.357", FEExpressionsNumericalApproximationElider]), Root[1-9 ((#1)^2)+9 ((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["0.756", FEExpressionsNumericalApproximationElider]), Root[1-84 ((#1)^2)+144 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-4.06", FEExpressionsNumericalApproximationElider]), Root[106929-10704 ((#1)^2)+256 ((#1)^4)&,2], ])≤0&&z (NumericalApproximation[Root, (RowDefault["-0.464", FEExpressionsNumericalApproximationElider]), Root[11881+22512 #1-6705 ((#1)^2)-216 ((#1)^3)+9 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["0.376", FEExpressionsNumericalApproximationElider]), Root[11881-26448 #1-13560 ((#1)^2)-576 ((#1)^3)+144 ((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["0.984", FEExpressionsNumericalApproximationElider]), Root[11881-7872 #1-4980 ((#1)^2)+576 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&z (NumericalApproximation[Root, (RowDefault["0.464", FEExpressionsNumericalApproximationElider]), Root[11881-22512 #1-6705 ((#1)^2)+216 ((#1)^3)+9 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["0.376", FEExpressionsNumericalApproximationElider]), Root[11881-26448 #1-13560 ((#1)^2)-576 ((#1)^3)+144 ((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["-0.984", FEExpressionsNumericalApproximationElider]), Root[11881+7872 #1-4980 ((#1)^2)-576 ((#1)^3)+144 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&(x/(2 (Sqrt[3])))+z (NumericalApproximation[Root, (RowDefault["-0.357", FEExpressionsNumericalApproximationElider]), Root[1-9 ((#1)^2)+9 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["-0.756", FEExpressionsNumericalApproximationElider]), Root[1-84 ((#1)^2)+144 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-4.06", FEExpressionsNumericalApproximationElider]), Root[106929-10704 ((#1)^2)+256 ((#1)^4)&,2], ])≤0&&z (NumericalApproximation[Root, (RowDefault["0.464", FEExpressionsNumericalApproximationElider]), Root[11881-22512 #1-6705 ((#1)^2)+216 ((#1)^3)+9 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["-0.376", FEExpressionsNumericalApproximationElider]), Root[11881+26448 #1-13560 ((#1)^2)+576 ((#1)^3)+144 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["0.984", FEExpressionsNumericalApproximationElider]), Root[11881-7872 #1-4980 ((#1)^2)+576 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&-(x/(2 (Sqrt[3])))+z (NumericalApproximation[Root, (RowDefault["-0.357", FEExpressionsNumericalApproximationElider]), Root[1-9 ((#1)^2)+9 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["0.756", FEExpressionsNumericalApproximationElider]), Root[1-84 ((#1)^2)+144 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-4.06", FEExpressionsNumericalApproximationElider]), Root[106929-10704 ((#1)^2)+256 ((#1)^4)&,2], ])≤0&&-(x/(2 (Sqrt[3])))+z (NumericalApproximation[Root, (RowDefault["0.357", FEExpressionsNumericalApproximationElider]), Root[1-9 ((#1)^2)+9 ((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["-0.756", FEExpressionsNumericalApproximationElider]), Root[1-84 ((#1)^2)+144 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-4.06", FEExpressionsNumericalApproximationElider]), Root[106929-10704 ((#1)^2)+256 ((#1)^4)&,2], ])≤0&&z (NumericalApproximation[Root, (RowDefault["-0.464", FEExpressionsNumericalApproximationElider]), Root[11881+22512 #1-6705 ((#1)^2)-216 ((#1)^3)+9 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["-0.984", FEExpressionsNumericalApproximationElider]), Root[11881+7872 #1-4980 ((#1)^2)-576 ((#1)^3)+144 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.376", FEExpressionsNumericalApproximationElider]), Root[11881+26448 #1-13560 ((#1)^2)+576 ((#1)^3)+144 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.752", FEExpressionsNumericalApproximationElider]), Root[11881-13224 #1-3390 ((#1)^2)-72 ((#1)^3)+9 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["0.232", FEExpressionsNumericalApproximationElider]), Root[11881-45024 #1-26820 ((#1)^2)+1728 ((#1)^3)+144 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.840", FEExpressionsNumericalApproximationElider]), Root[297025-318000 #1-44760 ((#1)^2)+2880 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.705", FEExpressionsNumericalApproximationElider]), Root[109-94 #1-85 ((#1)^2)-2 ((#1)^3)+((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["-0.788", FEExpressionsNumericalApproximationElider]), Root[2725+2300 #1-1540 ((#1)^2)-80 ((#1)^3)+16 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["0.218", FEExpressionsNumericalApproximationElider]), Root[109-324 #1-820 ((#1)^2)+48 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-4.96", FEExpressionsNumericalApproximationElider]), Root[104897349+12972744 #1-1627920 ((#1)^2)+4992 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.705", FEExpressionsNumericalApproximationElider]), Root[109+94 #1-85 ((#1)^2)+2 ((#1)^3)+((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["0.218", FEExpressionsNumericalApproximationElider]), Root[109-324 #1-820 ((#1)^2)+48 ((#1)^3)+16 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.788", FEExpressionsNumericalApproximationElider]), Root[2725-2300 #1-1540 ((#1)^2)+80 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-4.96", FEExpressionsNumericalApproximationElider]), Root[104897349+12972744 #1-1627920 ((#1)^2)+4992 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.752", FEExpressionsNumericalApproximationElider]), Root[11881+13224 #1-3390 ((#1)^2)+72 ((#1)^3)+9 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.840", FEExpressionsNumericalApproximationElider]), Root[297025+318000 #1-44760 ((#1)^2)-2880 ((#1)^3)+144 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["0.232", FEExpressionsNumericalApproximationElider]), Root[11881-45024 #1-26820 ((#1)^2)+1728 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.705", FEExpressionsNumericalApproximationElider]), Root[109-94 #1-85 ((#1)^2)-2 ((#1)^3)+((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["-0.218", FEExpressionsNumericalApproximationElider]), Root[109+324 #1-820 ((#1)^2)-48 ((#1)^3)+16 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["0.788", FEExpressionsNumericalApproximationElider]), Root[2725-2300 #1-1540 ((#1)^2)+80 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-4.96", FEExpressionsNumericalApproximationElider]), Root[104897349+12972744 #1-1627920 ((#1)^2)+4992 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.752", FEExpressionsNumericalApproximationElider]), Root[11881-13224 #1-3390 ((#1)^2)-72 ((#1)^3)+9 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["-0.840", FEExpressionsNumericalApproximationElider]), Root[297025+318000 #1-44760 ((#1)^2)-2880 ((#1)^3)+144 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.232", FEExpressionsNumericalApproximationElider]), Root[11881+45024 #1-26820 ((#1)^2)-1728 ((#1)^3)+144 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.752", FEExpressionsNumericalApproximationElider]), Root[11881+13224 #1-3390 ((#1)^2)+72 ((#1)^3)+9 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.232", FEExpressionsNumericalApproximationElider]), Root[11881+45024 #1-26820 ((#1)^2)-1728 ((#1)^3)+144 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["0.840", FEExpressionsNumericalApproximationElider]), Root[297025-318000 #1-44760 ((#1)^2)+2880 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.705", FEExpressionsNumericalApproximationElider]), Root[109+94 #1-85 ((#1)^2)+2 ((#1)^3)+((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.788", FEExpressionsNumericalApproximationElider]), Root[2725+2300 #1-1540 ((#1)^2)-80 ((#1)^3)+16 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.218", FEExpressionsNumericalApproximationElider]), Root[109+324 #1-820 ((#1)^2)-48 ((#1)^3)+16 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-4.96", FEExpressionsNumericalApproximationElider]), Root[104897349+12972744 #1-1627920 ((#1)^2)+4992 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&z (NumericalApproximation[Root, (RowDefault["0.752", FEExpressionsNumericalApproximationElider]), Root[11881-13224 #1-3390 ((#1)^2)-72 ((#1)^3)+9 ((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["0.232", FEExpressionsNumericalApproximationElider]), Root[11881-45024 #1-26820 ((#1)^2)+1728 ((#1)^3)+144 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["0.840", FEExpressionsNumericalApproximationElider]), Root[297025-318000 #1-44760 ((#1)^2)+2880 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&z (NumericalApproximation[Root, (RowDefault["-0.705", FEExpressionsNumericalApproximationElider]), Root[109+94 #1-85 ((#1)^2)+2 ((#1)^3)+((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["0.218", FEExpressionsNumericalApproximationElider]), Root[109-324 #1-820 ((#1)^2)+48 ((#1)^3)+16 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["0.788", FEExpressionsNumericalApproximationElider]), Root[2725-2300 #1-1540 ((#1)^2)+80 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-4.96", FEExpressionsNumericalApproximationElider]), Root[104897349+12972744 #1-1627920 ((#1)^2)+4992 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&z (NumericalApproximation[Root, (RowDefault["0.705", FEExpressionsNumericalApproximationElider]), Root[109-94 #1-85 ((#1)^2)-2 ((#1)^3)+((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["-0.218", FEExpressionsNumericalApproximationElider]), Root[109+324 #1-820 ((#1)^2)-48 ((#1)^3)+16 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["0.788", FEExpressionsNumericalApproximationElider]), Root[2725-2300 #1-1540 ((#1)^2)+80 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-4.96", FEExpressionsNumericalApproximationElider]), Root[104897349+12972744 #1-1627920 ((#1)^2)+4992 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&z (NumericalApproximation[Root, (RowDefault["-0.752", FEExpressionsNumericalApproximationElider]), Root[11881+13224 #1-3390 ((#1)^2)+72 ((#1)^3)+9 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["-0.232", FEExpressionsNumericalApproximationElider]), Root[11881+45024 #1-26820 ((#1)^2)-1728 ((#1)^3)+144 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["0.840", FEExpressionsNumericalApproximationElider]), Root[297025-318000 #1-44760 ((#1)^2)+2880 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&z (NumericalApproximation[Root, (RowDefault["0.705", FEExpressionsNumericalApproximationElider]), Root[109-94 #1-85 ((#1)^2)-2 ((#1)^3)+((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["-0.788", FEExpressionsNumericalApproximationElider]), Root[2725+2300 #1-1540 ((#1)^2)-80 ((#1)^3)+16 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["0.218", FEExpressionsNumericalApproximationElider]), Root[109-324 #1-820 ((#1)^2)+48 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-4.96", FEExpressionsNumericalApproximationElider]), Root[104897349+12972744 #1-1627920 ((#1)^2)+4992 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&z (NumericalApproximation[Root, (RowDefault["-0.752", FEExpressionsNumericalApproximationElider]), Root[11881+13224 #1-3390 ((#1)^2)+72 ((#1)^3)+9 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.840", FEExpressionsNumericalApproximationElider]), Root[297025+318000 #1-44760 ((#1)^2)-2880 ((#1)^3)+144 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["0.232", FEExpressionsNumericalApproximationElider]), Root[11881-45024 #1-26820 ((#1)^2)+1728 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&z (NumericalApproximation[Root, (RowDefault["0.752", FEExpressionsNumericalApproximationElider]), Root[11881-13224 #1-3390 ((#1)^2)-72 ((#1)^3)+9 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["-0.840", FEExpressionsNumericalApproximationElider]), Root[297025+318000 #1-44760 ((#1)^2)-2880 ((#1)^3)+144 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["-0.232", FEExpressionsNumericalApproximationElider]), Root[11881+45024 #1-26820 ((#1)^2)-1728 ((#1)^3)+144 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&z (NumericalApproximation[Root, (RowDefault["-0.705", FEExpressionsNumericalApproximationElider]), Root[109+94 #1-85 ((#1)^2)+2 ((#1)^3)+((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.788", FEExpressionsNumericalApproximationElider]), Root[2725+2300 #1-1540 ((#1)^2)-80 ((#1)^3)+16 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["-0.218", FEExpressionsNumericalApproximationElider]), Root[109+324 #1-820 ((#1)^2)-48 ((#1)^3)+16 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-4.96", FEExpressionsNumericalApproximationElider]), Root[104897349+12972744 #1-1627920 ((#1)^2)+4992 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["0.752", FEExpressionsNumericalApproximationElider]), Root[11881-13224 #1-3390 ((#1)^2)-72 ((#1)^3)+9 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.232", FEExpressionsNumericalApproximationElider]), Root[11881-45024 #1-26820 ((#1)^2)+1728 ((#1)^3)+144 ((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["0.840", FEExpressionsNumericalApproximationElider]), Root[297025-318000 #1-44760 ((#1)^2)+2880 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["0.705", FEExpressionsNumericalApproximationElider]), Root[109-94 #1-85 ((#1)^2)-2 ((#1)^3)+((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["-0.218", FEExpressionsNumericalApproximationElider]), Root[109+324 #1-820 ((#1)^2)-48 ((#1)^3)+16 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["0.788", FEExpressionsNumericalApproximationElider]), Root[2725-2300 #1-1540 ((#1)^2)+80 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-4.96", FEExpressionsNumericalApproximationElider]), Root[104897349+12972744 #1-1627920 ((#1)^2)+4992 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["0.705", FEExpressionsNumericalApproximationElider]), Root[109-94 #1-85 ((#1)^2)-2 ((#1)^3)+((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["-0.788", FEExpressionsNumericalApproximationElider]), Root[2725+2300 #1-1540 ((#1)^2)-80 ((#1)^3)+16 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["0.218", FEExpressionsNumericalApproximationElider]), Root[109-324 #1-820 ((#1)^2)+48 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-4.96", FEExpressionsNumericalApproximationElider]), Root[104897349+12972744 #1-1627920 ((#1)^2)+4992 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["0.752", FEExpressionsNumericalApproximationElider]), Root[11881-13224 #1-3390 ((#1)^2)-72 ((#1)^3)+9 ((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["-0.840", FEExpressionsNumericalApproximationElider]), Root[297025+318000 #1-44760 ((#1)^2)-2880 ((#1)^3)+144 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.232", FEExpressionsNumericalApproximationElider]), Root[11881+45024 #1-26820 ((#1)^2)-1728 ((#1)^3)+144 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-0.705", FEExpressionsNumericalApproximationElider]), Root[109+94 #1-85 ((#1)^2)+2 ((#1)^3)+((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["0.218", FEExpressionsNumericalApproximationElider]), Root[109-324 #1-820 ((#1)^2)+48 ((#1)^3)+16 ((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["0.788", FEExpressionsNumericalApproximationElider]), Root[2725-2300 #1-1540 ((#1)^2)+80 ((#1)^3)+16 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-4.96", FEExpressionsNumericalApproximationElider]), Root[104897349+12972744 #1-1627920 ((#1)^2)+4992 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-0.752", FEExpressionsNumericalApproximationElider]), Root[11881+13224 #1-3390 ((#1)^2)+72 ((#1)^3)+9 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.232", FEExpressionsNumericalApproximationElider]), Root[11881+45024 #1-26820 ((#1)^2)-1728 ((#1)^3)+144 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["0.840", FEExpressionsNumericalApproximationElider]), Root[297025-318000 #1-44760 ((#1)^2)+2880 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-0.752", FEExpressionsNumericalApproximationElider]), Root[11881+13224 #1-3390 ((#1)^2)+72 ((#1)^3)+9 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["-0.840", FEExpressionsNumericalApproximationElider]), Root[297025+318000 #1-44760 ((#1)^2)-2880 ((#1)^3)+144 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["0.232", FEExpressionsNumericalApproximationElider]), Root[11881-45024 #1-26820 ((#1)^2)+1728 ((#1)^3)+144 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-5.29", FEExpressionsNumericalApproximationElider]), Root[1270423449+202415616 #1-7052880 ((#1)^2)+19968 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-0.705", FEExpressionsNumericalApproximationElider]), Root[109+94 #1-85 ((#1)^2)+2 ((#1)^3)+((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["-0.788", FEExpressionsNumericalApproximationElider]), Root[2725+2300 #1-1540 ((#1)^2)-80 ((#1)^3)+16 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.218", FEExpressionsNumericalApproximationElider]), Root[109+324 #1-820 ((#1)^2)-48 ((#1)^3)+16 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-4.96", FEExpressionsNumericalApproximationElider]), Root[104897349+12972744 #1-1627920 ((#1)^2)+4992 ((#1)^3)+256 ((#1)^4)&,2], ])≤0&&x (NumericalApproximation[Root, (RowDefault["0.651", FEExpressionsNumericalApproximationElider]), Root[11881-22328 #1+6648 ((#1)^2)-608 ((#1)^3)+16 ((#1)^4)&,1], ])+y (NumericalApproximation[Root, (RowDefault["0.651", FEExpressionsNumericalApproximationElider]), Root[11881-22328 #1+6648 ((#1)^2)-608 ((#1)^3)+16 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["0.651", FEExpressionsNumericalApproximationElider]), Root[11881-22328 #1+6648 ((#1)^2)-608 ((#1)^3)+16 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&x (NumericalApproximation[Root, (RowDefault["0.651", FEExpressionsNumericalApproximationElider]), Root[11881-22328 #1+6648 ((#1)^2)-608 ((#1)^3)+16 ((#1)^4)&,1], ])+y (NumericalApproximation[Root, (RowDefault["0.651", FEExpressionsNumericalApproximationElider]), Root[11881-22328 #1+6648 ((#1)^2)-608 ((#1)^3)+16 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["-0.651", FEExpressionsNumericalApproximationElider]), Root[11881+22328 #1+6648 ((#1)^2)+608 ((#1)^3)+16 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&x (NumericalApproximation[Root, (RowDefault["0.651", FEExpressionsNumericalApproximationElider]), Root[11881-22328 #1+6648 ((#1)^2)-608 ((#1)^3)+16 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["0.651", FEExpressionsNumericalApproximationElider]), Root[11881-22328 #1+6648 ((#1)^2)-608 ((#1)^3)+16 ((#1)^4)&,1], ])+y (NumericalApproximation[Root, (RowDefault["-0.651", FEExpressionsNumericalApproximationElider]), Root[11881+22328 #1+6648 ((#1)^2)+608 ((#1)^3)+16 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&x (NumericalApproximation[Root, (RowDefault["0.651", FEExpressionsNumericalApproximationElider]), Root[11881-22328 #1+6648 ((#1)^2)-608 ((#1)^3)+16 ((#1)^4)&,1], ])+y (NumericalApproximation[Root, (RowDefault["-0.651", FEExpressionsNumericalApproximationElider]), Root[11881+22328 #1+6648 ((#1)^2)+608 ((#1)^3)+16 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["-0.651", FEExpressionsNumericalApproximationElider]), Root[11881+22328 #1+6648 ((#1)^2)+608 ((#1)^3)+16 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.651", FEExpressionsNumericalApproximationElider]), Root[11881-22328 #1+6648 ((#1)^2)-608 ((#1)^3)+16 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["0.651", FEExpressionsNumericalApproximationElider]), Root[11881-22328 #1+6648 ((#1)^2)-608 ((#1)^3)+16 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["-0.651", FEExpressionsNumericalApproximationElider]), Root[11881+22328 #1+6648 ((#1)^2)+608 ((#1)^3)+16 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.651", FEExpressionsNumericalApproximationElider]), Root[11881-22328 #1+6648 ((#1)^2)-608 ((#1)^3)+16 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["-0.651", FEExpressionsNumericalApproximationElider]), Root[11881+22328 #1+6648 ((#1)^2)+608 ((#1)^3)+16 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["-0.651", FEExpressionsNumericalApproximationElider]), Root[11881+22328 #1+6648 ((#1)^2)+608 ((#1)^3)+16 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&z (NumericalApproximation[Root, (RowDefault["0.651", FEExpressionsNumericalApproximationElider]), Root[11881-22328 #1+6648 ((#1)^2)-608 ((#1)^3)+16 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["-0.651", FEExpressionsNumericalApproximationElider]), Root[11881+22328 #1+6648 ((#1)^2)+608 ((#1)^3)+16 ((#1)^4)&,4], ])+y (NumericalApproximation[Root, (RowDefault["-0.651", FEExpressionsNumericalApproximationElider]), Root[11881+22328 #1+6648 ((#1)^2)+608 ((#1)^3)+16 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-0.651", FEExpressionsNumericalApproximationElider]), Root[11881+22328 #1+6648 ((#1)^2)+608 ((#1)^3)+16 ((#1)^4)&,4], ])+y (NumericalApproximation[Root, (RowDefault["-0.651", FEExpressionsNumericalApproximationElider]), Root[11881+22328 #1+6648 ((#1)^2)+608 ((#1)^3)+16 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["-0.651", FEExpressionsNumericalApproximationElider]), Root[11881+22328 #1+6648 ((#1)^2)+608 ((#1)^3)+16 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-5.17", FEExpressionsNumericalApproximationElider]), Root[-128207871-30425832 #1-1097040 ((#1)^2)-384 ((#1)^3)+256 ((#1)^4)&,3], ])≤0;

FullSimplify[reg]//Timing

SimplePolyhedron

SimplePolyhedronQ[p]

Skeleton

PolyhedronData[pname,"Skeleton"]

PolyhedronData[pname,"Skeleton","Name"]

GraphData["TruncatedPentakisDodecahedralGraph"]

With[{faces=PolyhedronData["TruncatedPentakisDodecahedron","FaceIndices"],verts=PolyhedronData["TruncatedPentakisDodecahedron","Vertices"]},
ToCommonEdges[GraphData["TruncatedPentakisDodecahedralGraph"],Graph[Range[Length[verts]],UndirectedEdge@@@Union[Sort/@Flatten[Partition[#,2,1,1]&/@faces,1]]]]
]//Chop//N

SurfaceArea

PolyhedronData[pname,"SurfaceArea"]

FullSimplify[%]

(s=SurfaceArea[p])//Timing

ToAlgebraicRoot[s,WorkingPrecision->5000]//Quiet

FullSimplify[%]

ToAlgebraicRoot[Total[Area/@PolyhedronData[pname,"Polygons"]],WorkingPrecision->5000]//Quiet//Timing

VertexCount

PolyhedronData[pname,"VertexCount"]

VertexSubsetHulls

PolyhedronData[pname,"VertexSubsetHulls"]

Platonic

(h=VertexSubsetHulls[p,"Platonic","Skip"->{}])//Timing

Volume

PolyhedronData[pname,"Volume"]

(v=Volume[p]//FullSimplify)//Timing

N[v]

ToAlgebraicRoot[PolyhedronVolume[p]]//FullSimplify//Timing

Perspective projections

gs=PolyhedronProjectionGraph[PolyhedronData["TruncatedPentakisDodecahedron","Polyhedron"],#]&/@{{0,1,0},{1,0,1},{1,1,1}}

Manipulate[PolyhedronProjectionGraph[N@PolyhedronData["TruncatedPentakisDodecahedron","Polyhedron"],{a,b,c}],{a,-1,1},{b,-1,1},{c,-1,1}]

{1, 0, 0} [rotated {0,1,0}]

PolyhedronProjectionGraph[PolyhedronData["TruncatedPentakisDodecahedron","Polyhedron"],{1,0.001,0}]

{0, 1, 0}

PolyhedronProjectionGraph[PolyhedronData["TruncatedPentakisDodecahedron","Polyhedron"],{0,1,0}]

{0, 0, 1} [rotated {0, 1, 0}]

PolyhedronProjectionGraph[PolyhedronData["TruncatedPentakisDodecahedron","Polyhedron"],{0,0,1}]

{1, 1, 1}

PolyhedronProjectionGraph[PolyhedronData["TruncatedPentakisDodecahedron","Polyhedron"],{1,1,1}]

{0, 1, 1} [rotated {1, 0, 1}]

PolyhedronProjectionGraph[PolyhedronData["TruncatedPentakisDodecahedron","Polyhedron"],{0,1,1}]

{1, 0, 1}

PolyhedronProjectionGraph[PolyhedronData["TruncatedPentakisDodecahedron","Polyhedron"],{1,0,1}]

{1, 1, 0} [rotated {1, 0, 1}]

PolyhedronProjectionGraph[PolyhedronData["TruncatedPentakisDodecahedron","Polyhedron"],{1,1,0}]

Construction

http://dmccooey.com/polyhedra/TruncatedPentakisDodecahedron1.txt

C0=(Sqrt[15]-1-Sqrt[3])/2;
C1=(1+Sqrt[5])/4;
C2=(3 Sqrt[5]-3-Sqrt[3])/2;
C3=(6-7 Sqrt[3]+5 Sqrt[15])/12;
C4=(3+9 Sqrt[3]+3 Sqrt[5]-Sqrt[15])/12;
C5=3 (Sqrt[5]-1)/2;
C6=(2 Sqrt[3]-7+5 Sqrt[5])/4;
C7=(10-3 Sqrt[3]+Sqrt[15])/4;
C8=(11+3 Sqrt[3]-Sqrt[5]-Sqrt[15])/4;
C9=(7 Sqrt[5]-5)/4;
C10=(21-5 Sqrt[3]+Sqrt[15])/6;
C11=(3 Sqrt[3]-15+21 Sqrt[5]-Sqrt[15])/12;
C12=(7 Sqrt[5]-3)/4;
C13=(39+6 Sqrt[3]+3 Sqrt[5]-4 Sqrt[15])/12;
C14=(5+Sqrt[3]+5 Sqrt[5]-Sqrt[15])/4;
C15=(13+Sqrt[5])/4;
C16=(21 Sqrt[5]-9-4 Sqrt[3]+4 Sqrt[15])/12;
C17=(3-Sqrt[3]+5 Sqrt[5]+Sqrt[15])/4;
C18=(15+Sqrt[5])/4;
C19=(45-Sqrt[3]+3 Sqrt[5]+Sqrt[15])/12;
C20=(21-Sqrt[5])/4;

V0={0,C0,C20};
V1={0,C0,-C20};
V2={0,-C0,C20};
V3={0,-C0,-C20};
V4={C20,0,C0};
V5={C20,0,-C0};
V6={-C20,0,C0};
V7={-C20,0,-C0};
V8={C0,C20,0};
V9={C0,-C20,0};
V10={-C0,C20,0};
V11={-C0,-C20,0};
V12={C2,C3,C19};
V13={C2,C3,-C19};
V14={C2,-C3,C19};
V15={C2,-C3,-C19};
V16={-C2,C3,C19};
V17={-C2,C3,-C19};
V18={-C2,-C3,C19};
V19={-C2,-C3,-C19};
V20={C19,C2,C3};
V21={C19,C2,-C3};
V22={C19,-C2,C3};
V23={C19,-C2,-C3};
V24={-C19,C2,C3};
V25={-C19,C2,-C3};
V26={-C19,-C2,C3};
V27={-C19,-C2,-C3};
V28={C3,C19,C2};
V29={C3,C19,-C2};
V30={C3,-C19,C2};
V31={C3,-C19,-C2};
V32={-C3,C19,C2};
V33={-C3,C19,-C2};
V34={-C3,-C19,C2};
V35={-C3,-C19,-C2};
V36={C5,1/2,C18};
V37={C5,1/2,-C18};
V38={C5,-1/2,C18};
V39={C5,-1/2,-C18};
V40={-C5,1/2,C18};
V41={-C5,1/2,-C18};
V42={-C5,-1/2,C18};
V43={-C5,-1/2,-C18};
V44={C18,C5,1/2};
V45={C18,C5,-1/2};
V46={C18,-C5,1/2};
V47={C18,-C5,-1/2};
V48={-C18,C5,1/2};
V49={-C18,C5,-1/2};
V50={-C18,-C5,1/2};
V51={-C18,-C5,-1/2};
V52={1/2,C18,C5};
V53={1/2,C18,-C5};
V54={1/2,-C18,C5};
V55={1/2,-C18,-C5};
V56={-1/2,C18,C5};
V57={-1/2,C18,-C5};
V58={-1/2,-C18,C5};
V59={-1/2,-C18,-C5};
V60={C2,C7,C17};
V61={C2,C7,-C17};
V62={C2,-C7,C17};
V63={C2,-C7,-C17};
V64={-C2,C7,C17};
V65={-C2,C7,-C17};
V66={-C2,-C7,C17};
V67={-C2,-C7,-C17};
V68={C17,C2,C7};
V69={C17,C2,-C7};
V70={C17,-C2,C7};
V71={C17,-C2,-C7};
V72={-C17,C2,C7};
V73={-C17,C2,-C7};
V74={-C17,-C2,C7};
V75={-C17,-C2,-C7};
V76={C7,C17,C2};
V77={C7,C17,-C2};
V78={C7,-C17,C2};
V79={C7,-C17,-C2};
V80={-C7,C17,C2};
V81={-C7,C17,-C2};
V82={-C7,-C17,C2};
V83={-C7,-C17,-C2};
V84={0,C10,C16};
V85={0,C10,-C16};
V86={0,-C10,C16};
V87={0,-C10,-C16};
V88={C16,0,C10};
V89={C16,0,-C10};
V90={-C16,0,C10};
V91={-C16,0,-C10};
V92={C10,C16,0};
V93={C10,-C16,0};
V94={-C10,C16,0};
V95={-C10,-C16,0};
V96={C9,C1,C15};
V97={C9,C1,-C15};
V98={C9,-C1,C15};
V99={C9,-C1,-C15};
V100={-C9,C1,C15};
V101={-C9,C1,-C15};
V102={-C9,-C1,C15};
V103={-C9,-C1,-C15};
V104={C15,C9,C1};
V105={C15,C9,-C1};
V106={C15,-C9,C1};
V107={C15,-C9,-C1};
V108={-C15,C9,C1};
V109={-C15,C9,-C1};
V110={-C15,-C9,C1};
V111={-C15,-C9,-C1};
V112={C1,C15,C9};
V113={C1,C15,-C9};
V114={C1,-C15,C9};
V115={C1,-C15,-C9};
V116={-C1,C15,C9};
V117={-C1,C15,-C9};
V118={-C1,-C15,C9};
V119={-C1,-C15,-C9};
V120={C6,C8,C14};
V121={C6,C8,-C14};
V122={C6,-C8,C14};
V123={C6,-C8,-C14};
V124={-C6,C8,C14};
V125={-C6,C8,-C14};
V126={-C6,-C8,C14};
V127={-C6,-C8,-C14};
V128={C14,C6,C8};
V129={C14,C6,-C8};
V130={C14,-C6,C8};
V131={C14,-C6,-C8};
V132={-C14,C6,C8};
V133={-C14,C6,-C8};
V134={-C14,-C6,C8};
V135={-C14,-C6,-C8};
V136={C8,C14,C6};
V137={C8,C14,-C6};
V138={C8,-C14,C6};
V139={C8,-C14,-C6};
V140={-C8,C14,C6};
V141={-C8,C14,-C6};
V142={-C8,-C14,C6};
V143={-C8,-C14,-C6};
V144={C12,0,7/2};
V145={C12,0,-7/2};
V146={-C12,0,7/2};
V147={-C12,0,-7/2};
V148={7/2,C12,0};
V149={7/2,-C12,0};
V150={-7/2,C12,0};
V151={-7/2,-C12,0};
V152={0,7/2,C12};
V153={0,7/2,-C12};
V154={0,-7/2,C12};
V155={0,-7/2,-C12};
V156={C11,C4,C13};
V157={C11,C4,-C13};
V158={C11,-C4,C13};
V159={C11,-C4,-C13};
V160={-C11,C4,C13};
V161={-C11,C4,-C13};
V162={-C11,-C4,C13};
V163={-C11,-C4,-C13};
V164={C13,C11,C4};
V165={C13,C11,-C4};
V166={C13,-C11,C4};
V167={C13,-C11,-C4};
V168={-C13,C11,C4};
V169={-C13,C11,-C4};
V170={-C13,-C11,C4};
V171={-C13,-C11,-C4};
V172={C4,C13,C11};
V173={C4,C13,-C11};
V174={C4,-C13,C11};
V175={C4,-C13,-C11};
V176={-C4,C13,C11};
V177={-C4,C13,-C11};
V178={-C4,-C13,C11};
V179={-C4,-C13,-C11};

vertices=Symbol/@Table["V"<>ToString[n],{n,0,179}]

faces=Sort[1+{{0,12,60,84,64,16},{1,17,65,85,61,13},{2,18,66,86,62,14},{3,15,63,87,67,19},{4,20,68,88,70,22},{5,23,71,89,69,21},{6,26,74,90,72,24},{7,25,73,91,75,27},{8,28,76,92,77,29},{9,31,79,93,78,30},{10,33,81,94,80,32},{11,34,82,95,83,35},{120,156,128,164,136,172},{121,173,137,165,129,157},{122,174,138,166,130,158},{123,159,131,167,139,175},{124,176,140,168,132,160},{125,161,133,169,141,177},{126,162,134,170,142,178},{127,179,143,171,135,163},{0,2,14,38,36,12},{1,3,19,43,41,17},{2,0,16,40,42,18},{3,1,13,37,39,15},{4,5,21,45,44,20},{5,4,22,46,47,23},{6,7,27,51,50,26},{7,6,24,48,49,25},{8,10,32,56,52,28},{9,11,35,59,55,31},{10,8,29,53,57,33},{11,9,30,54,58,34},{12,36,96,156,120,60},{13,61,121,157,97,37},{14,62,122,158,98,38},{15,39,99,159,123,63},{16,64,124,160,100,40},{17,41,101,161,125,65},{18,42,102,162,126,66},{19,67,127,163,103,43},{20,44,104,164,128,68},{21,69,129,165,105,45},{22,70,130,166,106,46},{23,47,107,167,131,71},{24,72,132,168,108,48},{25,49,109,169,133,73},{26,50,110,170,134,74},{27,75,135,171,111,51},{28,52,112,172,136,76},{29,77,137,173,113,53},{30,78,138,174,114,54},{31,55,115,175,139,79},{32,80,140,176,116,56},{33,57,117,177,141,81},{34,58,118,178,142,82},{35,83,143,179,119,59},{60,120,172,112,152,84},{61,85,153,113,173,121},{62,86,154,114,174,122},{63,123,175,115,155,87},{64,84,152,116,176,124},{65,125,177,117,153,85},{66,126,178,118,154,86},{67,87,155,119,179,127},{68,128,156,96,144,88},{69,89,145,97,157,129},{70,88,144,98,158,130},{71,131,159,99,145,89},{72,90,146,100,160,132},{73,133,161,101,147,91},{74,134,162,102,146,90},{75,91,147,103,163,135},{76,136,164,104,148,92},{77,92,148,105,165,137},{78,93,149,106,166,138},{79,139,167,107,149,93},{80,94,150,108,168,140},{81,141,169,109,150,94},{82,142,170,110,151,95},{83,95,151,111,171,143},{144,96,36,38,98},{145,99,39,37,97},{146,102,42,40,100},{147,101,41,43,103},{148,104,44,45,105},{149,107,47,46,106},{150,109,49,48,108},{151,110,50,51,111},{152,112,52,56,116},{153,117,57,53,113},{154,118,58,54,114},{155,115,55,59,119}}];

poly=Polyhedron[vertices,faces]

Graphics3D[{FaceForm[Green,Red],poly}]

SimplePolyhedronQ[poly]

SortBy[SimplifyNumericallyDistinct[PolyhedronEdgeLengths[poly]],N]//Tally//Quiet

N[%[[All,1]]]

(sphere=Midsphere[poly,Method->"PointLineDistance"]//FullSimplify)//Timing

Graphics3D[{Opacity[.5],Red,poly,Yellow,sphere}]

Net construction

Graphics[{EdgeForm[Black],FaceForm[LightYellow],net=UnfoldPolyhedron[PolyhedronData["TruncatedPentakisDodecahedron","Polyhedron"],WorkingPrecision->10000]}]//Timing

net[[1,1,1]]//Precision

f=Sort[net[[2]]]

i=0;
v=net[[1]];
n=Length[Flatten[v]];
Monitor[vexact=Map[
ToAlgebraicRoot[++i;#,WorkingPrecision->2000]&,
v,
{2}
],
Column[{Row[{i,"/",n}],ProgressIndicator[i,{1,n}]}]
];//Timing

ToAlgebraicRoot[Total[Area[Polygon[vexact,#]]&/@f],WorkingPrecision->2000]

PolyhedronData["TruncatedPentakisDodecahedron","SurfaceArea"]

vfinal=Union[vexact];

ffinal=Sort[vexact[[#]]&/@f/.Thread[vfinal->Range[Length[vfinal]]]]

Graphics[{FaceForm[LightYellow,Red],EdgeForm[Black],Polygon[vfinal,ffinal]},Axes->True]

ToAlgebraicRoot[Total[Area[Polygon[vfinal,#]]&/@ffinal],WorkingPrecision->2000]

PolyhedronData["TruncatedPentakisDodecahedron","SurfaceArea"]

vfinal//FullSimplify

PolyhedronData

PolyhedronDataString

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

WriteString[file,PolyhedronDataString[poly,
"StandardName"->"TruncatedPentakisDodecahedron",
"Name"->"truncated pentakis dodecahedron"
]]

Close[file]