Pentakis Icosidodecahedron

Author

Eric W. Weisstein
August 15, 2022

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

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

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

Source

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

Dual of the chamfered dodecahedron

Figure

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

Solid

PolyhedronData["PentakisIcosidodecahedron","Orientations"]

PolyhedronData["PentakisIcosidodecahedron"]

Show[PolyhedronData[{"PentakisIcosidodecahedron",#}],Boxed->False]&/@PolyhedronData["PentakisIcosidodecahedron","Orientations"]

Solid and Dual

PolyhedronData["PentakisIcosidodecahedron","Dual","Name"]

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

With[{pname="PentakisIcosidodecahedron"},
Graphics3D[{Opacity[.5],
{Red,PolyhedronData[pname,"Polyhedron"]},
{Green,PolyhedronData[pname,"Dual","Polyhedron"]},
{Yellow,PolyhedronData[pname,"Midsphere"]}
}]]

Net

PolyhedronData["PentakisIcosidodecahedron","Net"]

PolyhedronData["PentakisIcosidodecahedron","Net","Colored"]

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

(canonical) "PentakisIcosidodecahedron" Properties

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

Centroid

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

PolyhedronData[pname,"Centroid"]

ToAlgebraicRoot/@RegionCentroid[p]//Quiet

(xbar=PolyhedronCentroid[p])//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

DualScale

polyrho=PolyhedronData[pname,"Midradius"];
dualrho=PolyhedronData["CanonicalChamferedDodecahedron","Midradius"];

(polyrho/dualrho)//RootReduce//FullSimplify

N[%]

1/(1/8) (-5+(Sqrt[5])+2 (Sqrt[2 (5+(Sqrt[5]))]))//FullSimplify

EdgeCount

PolyhedronData[pname,"EdgeCount"]

EdgeLengths

PolyhedronData[pname,"EdgeLengths"]

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

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}])/vol))//Timing

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

(i=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)//ToAlgebraicRoot//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])/vol))//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)//ToAlgebraicRoot//FullSimplify)//Timing

N[i]

Midsphere

sphere=PolyhedronData[pname,"Midsphere"]

(sphere=Midsphere[N@p])//Timing

(sphere=Midsphere[N[p,200]])//Timing

ToAlgebraicRoot@sphere[[2]]//FullSimplify

N[%]

(sphere=Midsphere[p])//Timing

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

FullSimplify[sphere]

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

Net

PolyhedronData[pname,"Net"]

Region

PolyhedronData[pname,"Region"]

RegionFunction

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

ineq=y (NumericalApproximation[Root, (RowDefault["0.403", FEExpressionsNumericalApproximationElider]), Root[361-1936 #1-2624 ((#1)^2)+11264 ((#1)^3)+4096 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["0.898", FEExpressionsNumericalApproximationElider]), Root[361+4160 #1-3200 ((#1)^2)-20480 ((#1)^3)+20480 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["-0.555", FEExpressionsNumericalApproximationElider]), Root[361+1440 #1-10560 ((#1)^2)-10240 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.403", FEExpressionsNumericalApproximationElider]), Root[361+1936 #1-2624 ((#1)^2)-11264 ((#1)^3)+4096 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["0.898", FEExpressionsNumericalApproximationElider]), Root[361+4160 #1-3200 ((#1)^2)-20480 ((#1)^3)+20480 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["-0.555", FEExpressionsNumericalApproximationElider]), Root[361+1440 #1-10560 ((#1)^2)-10240 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.403", FEExpressionsNumericalApproximationElider]), Root[361+1936 #1-2624 ((#1)^2)-11264 ((#1)^3)+4096 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["0.555", FEExpressionsNumericalApproximationElider]), Root[361-1440 #1-10560 ((#1)^2)+10240 ((#1)^3)+20480 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["-0.898", FEExpressionsNumericalApproximationElider]), Root[361-4160 #1-3200 ((#1)^2)+20480 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.403", FEExpressionsNumericalApproximationElider]), Root[361-1936 #1-2624 ((#1)^2)+11264 ((#1)^3)+4096 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["0.555", FEExpressionsNumericalApproximationElider]), Root[361-1440 #1-10560 ((#1)^2)+10240 ((#1)^3)+20480 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["-0.898", FEExpressionsNumericalApproximationElider]), Root[361-4160 #1-3200 ((#1)^2)+20480 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&x (NumericalApproximation[Root, (RowDefault["0.686", FEExpressionsNumericalApproximationElider]), Root[361+1360 #1-720 ((#1)^2)-3840 ((#1)^3)+1280 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.898", FEExpressionsNumericalApproximationElider]), Root[361+4160 #1-3200 ((#1)^2)-20480 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&x (NumericalApproximation[Root, (RowDefault["1.11", FEExpressionsNumericalApproximationElider]), Root[361-720 #1-2640 ((#1)^2)+1280 ((#1)^3)+1280 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["0.212", FEExpressionsNumericalApproximationElider]), Root[361+1280 #1-23680 ((#1)^2)+40960 ((#1)^3)+20480 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-0.686", FEExpressionsNumericalApproximationElider]), Root[361-1360 #1-720 ((#1)^2)+3840 ((#1)^3)+1280 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.898", FEExpressionsNumericalApproximationElider]), Root[361-4160 #1-3200 ((#1)^2)+20480 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-1.11", FEExpressionsNumericalApproximationElider]), Root[361+720 #1-2640 ((#1)^2)-1280 ((#1)^3)+1280 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["-0.212", FEExpressionsNumericalApproximationElider]), Root[361-1280 #1-23680 ((#1)^2)-40960 ((#1)^3)+20480 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["1.06", FEExpressionsNumericalApproximationElider]), Root[361+1456 #1-5184 ((#1)^2)-1024 ((#1)^3)+4096 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["0.343", FEExpressionsNumericalApproximationElider]), Root[361+2720 #1-2880 ((#1)^2)-30720 ((#1)^3)+20480 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.212", FEExpressionsNumericalApproximationElider]), Root[361+1280 #1-23680 ((#1)^2)+40960 ((#1)^3)+20480 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["1.06", FEExpressionsNumericalApproximationElider]), Root[361+1456 #1-5184 ((#1)^2)-1024 ((#1)^3)+4096 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["-0.212", FEExpressionsNumericalApproximationElider]), Root[361-1280 #1-23680 ((#1)^2)-40960 ((#1)^3)+20480 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.343", FEExpressionsNumericalApproximationElider]), Root[361-2720 #1-2880 ((#1)^2)+30720 ((#1)^3)+20480 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-1.06", FEExpressionsNumericalApproximationElider]), Root[361-1456 #1-5184 ((#1)^2)+1024 ((#1)^3)+4096 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["0.343", FEExpressionsNumericalApproximationElider]), Root[361+2720 #1-2880 ((#1)^2)-30720 ((#1)^3)+20480 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.212", FEExpressionsNumericalApproximationElider]), Root[361+1280 #1-23680 ((#1)^2)+40960 ((#1)^3)+20480 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-1.06", FEExpressionsNumericalApproximationElider]), Root[361-1456 #1-5184 ((#1)^2)+1024 ((#1)^3)+4096 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["-0.212", FEExpressionsNumericalApproximationElider]), Root[361-1280 #1-23680 ((#1)^2)-40960 ((#1)^3)+20480 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.343", FEExpressionsNumericalApproximationElider]), Root[361-2720 #1-2880 ((#1)^2)+30720 ((#1)^3)+20480 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.159", FEExpressionsNumericalApproximationElider]), Root[-19-64 #1+896 ((#1)^2)+4096 ((#1)^3)+4096 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.898", FEExpressionsNumericalApproximationElider]), Root[361+4160 #1-3200 ((#1)^2)-20480 ((#1)^3)+20480 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["-0.219", FEExpressionsNumericalApproximationElider]), Root[-19+480 #1-640 ((#1)^2)-10240 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.159", FEExpressionsNumericalApproximationElider]), Root[-19+64 #1+896 ((#1)^2)-4096 ((#1)^3)+4096 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["0.898", FEExpressionsNumericalApproximationElider]), Root[361+4160 #1-3200 ((#1)^2)-20480 ((#1)^3)+20480 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["-0.219", FEExpressionsNumericalApproximationElider]), Root[-19+480 #1-640 ((#1)^2)-10240 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.258", FEExpressionsNumericalApproximationElider]), Root[-19-288 #1-576 ((#1)^2)+2048 ((#1)^3)+4096 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["0.898", FEExpressionsNumericalApproximationElider]), Root[361+4160 #1-3200 ((#1)^2)-20480 ((#1)^3)+20480 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["0.0837", FEExpressionsNumericalApproximationElider]), Root[-19-80 #1+2240 ((#1)^2)+15360 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.258", FEExpressionsNumericalApproximationElider]), Root[-19+288 #1-576 ((#1)^2)-2048 ((#1)^3)+4096 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.898", FEExpressionsNumericalApproximationElider]), Root[361+4160 #1-3200 ((#1)^2)-20480 ((#1)^3)+20480 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["0.0837", FEExpressionsNumericalApproximationElider]), Root[-19-80 #1+2240 ((#1)^2)+15360 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&x (NumericalApproximation[Root, (RowDefault["0.271", FEExpressionsNumericalApproximationElider]), Root[-19+200 #1-400 ((#1)^2)-640 ((#1)^3)+1280 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.898", FEExpressionsNumericalApproximationElider]), Root[361+4160 #1-3200 ((#1)^2)-20480 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.159", FEExpressionsNumericalApproximationElider]), Root[-19+64 #1+896 ((#1)^2)-4096 ((#1)^3)+4096 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["0.705", FEExpressionsNumericalApproximationElider]), Root[-19-1280 #1-8320 ((#1)^2)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.258", FEExpressionsNumericalApproximationElider]), Root[-19+288 #1-576 ((#1)^2)-2048 ((#1)^3)+4096 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["-0.327", FEExpressionsNumericalApproximationElider]), Root[-19+1120 #1-1920 ((#1)^2)-10240 ((#1)^3)+20480 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["0.840", FEExpressionsNumericalApproximationElider]), Root[1121+80 #1-11840 ((#1)^2)-5120 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.159", FEExpressionsNumericalApproximationElider]), Root[-19-64 #1+896 ((#1)^2)+4096 ((#1)^3)+4096 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["-0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["0.705", FEExpressionsNumericalApproximationElider]), Root[-19-1280 #1-8320 ((#1)^2)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&x (NumericalApproximation[Root, (RowDefault["0.924", FEExpressionsNumericalApproximationElider]), Root[-19-128 #1-176 ((#1)^2)+128 ((#1)^3)+256 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["-0.159", FEExpressionsNumericalApproximationElider]), Root[-19-64 #1+896 ((#1)^2)+4096 ((#1)^3)+4096 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.258", FEExpressionsNumericalApproximationElider]), Root[-19-288 #1-576 ((#1)^2)+2048 ((#1)^3)+4096 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.327", FEExpressionsNumericalApproximationElider]), Root[-19+1120 #1-1920 ((#1)^2)-10240 ((#1)^3)+20480 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["0.840", FEExpressionsNumericalApproximationElider]), Root[1121+80 #1-11840 ((#1)^2)-5120 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.159", FEExpressionsNumericalApproximationElider]), Root[-19+64 #1+896 ((#1)^2)-4096 ((#1)^3)+4096 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["-0.705", FEExpressionsNumericalApproximationElider]), Root[-19+1280 #1-8320 ((#1)^2)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.258", FEExpressionsNumericalApproximationElider]), Root[-19+288 #1-576 ((#1)^2)-2048 ((#1)^3)+4096 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["-0.840", FEExpressionsNumericalApproximationElider]), Root[1121-80 #1-11840 ((#1)^2)+5120 ((#1)^3)+20480 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["0.327", FEExpressionsNumericalApproximationElider]), Root[-19-1120 #1-1920 ((#1)^2)+10240 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.159", FEExpressionsNumericalApproximationElider]), Root[-19-64 #1+896 ((#1)^2)+4096 ((#1)^3)+4096 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["-0.705", FEExpressionsNumericalApproximationElider]), Root[-19+1280 #1-8320 ((#1)^2)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-0.924", FEExpressionsNumericalApproximationElider]), Root[-19+128 #1-176 ((#1)^2)-128 ((#1)^3)+256 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["0.159", FEExpressionsNumericalApproximationElider]), Root[-19+64 #1+896 ((#1)^2)-4096 ((#1)^3)+4096 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.258", FEExpressionsNumericalApproximationElider]), Root[-19-288 #1-576 ((#1)^2)+2048 ((#1)^3)+4096 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.840", FEExpressionsNumericalApproximationElider]), Root[1121-80 #1-11840 ((#1)^2)+5120 ((#1)^3)+20480 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["0.327", FEExpressionsNumericalApproximationElider]), Root[-19-1120 #1-1920 ((#1)^2)+10240 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.159", FEExpressionsNumericalApproximationElider]), Root[-19-64 #1+896 ((#1)^2)+4096 ((#1)^3)+4096 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["0.219", FEExpressionsNumericalApproximationElider]), Root[-19-480 #1-640 ((#1)^2)+10240 ((#1)^3)+20480 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["-0.898", FEExpressionsNumericalApproximationElider]), Root[361-4160 #1-3200 ((#1)^2)+20480 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.159", FEExpressionsNumericalApproximationElider]), Root[-19+64 #1+896 ((#1)^2)-4096 ((#1)^3)+4096 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["0.219", FEExpressionsNumericalApproximationElider]), Root[-19-480 #1-640 ((#1)^2)+10240 ((#1)^3)+20480 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["-0.898", FEExpressionsNumericalApproximationElider]), Root[361-4160 #1-3200 ((#1)^2)+20480 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.258", FEExpressionsNumericalApproximationElider]), Root[-19-288 #1-576 ((#1)^2)+2048 ((#1)^3)+4096 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.0837", FEExpressionsNumericalApproximationElider]), Root[-19+80 #1+2240 ((#1)^2)-15360 ((#1)^3)+20480 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["-0.898", FEExpressionsNumericalApproximationElider]), Root[361-4160 #1-3200 ((#1)^2)+20480 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.258", FEExpressionsNumericalApproximationElider]), Root[-19+288 #1-576 ((#1)^2)-2048 ((#1)^3)+4096 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["-0.0837", FEExpressionsNumericalApproximationElider]), Root[-19+80 #1+2240 ((#1)^2)-15360 ((#1)^3)+20480 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["-0.898", FEExpressionsNumericalApproximationElider]), Root[361-4160 #1-3200 ((#1)^2)+20480 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-0.271", FEExpressionsNumericalApproximationElider]), Root[-19-200 #1-400 ((#1)^2)+640 ((#1)^3)+1280 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.898", FEExpressionsNumericalApproximationElider]), Root[361-4160 #1-3200 ((#1)^2)+20480 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.286", FEExpressionsNumericalApproximationElider]), Root[-19+112 #1+384 ((#1)^2)-3072 ((#1)^3)+4096 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["0.831", FEExpressionsNumericalApproximationElider]), Root[361-4560 #1-13440 ((#1)^2)+5120 ((#1)^3)+20480 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["0.327", FEExpressionsNumericalApproximationElider]), Root[-19-1120 #1-1920 ((#1)^2)+10240 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.286", FEExpressionsNumericalApproximationElider]), Root[-19+112 #1+384 ((#1)^2)-3072 ((#1)^3)+4096 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["0.664", FEExpressionsNumericalApproximationElider]), Root[-779+2640 #1+5760 ((#1)^2)-25600 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.543", FEExpressionsNumericalApproximationElider]), Root[-95+160 #1+1600 ((#1)^2)-5120 ((#1)^3)+4096 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.159", FEExpressionsNumericalApproximationElider]), Root[-19+64 #1+896 ((#1)^2)-4096 ((#1)^3)+4096 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["0.747", FEExpressionsNumericalApproximationElider]), Root[-19+368 #1-1216 ((#1)^2)-2048 ((#1)^3)+4096 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.543", FEExpressionsNumericalApproximationElider]), Root[-95+160 #1+1600 ((#1)^2)-5120 ((#1)^3)+4096 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["0.477", FEExpressionsNumericalApproximationElider]), Root[-19+720 #1-6080 ((#1)^2)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&(1/16) (9+(Sqrt[5])) y+x (NumericalApproximation[Root, (RowDefault["0.528", FEExpressionsNumericalApproximationElider]), Root[-19-480 #1+6080 ((#1)^2)-20480 ((#1)^3)+20480 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["0.327", FEExpressionsNumericalApproximationElider]), Root[-19-1120 #1-1920 ((#1)^2)+10240 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.286", FEExpressionsNumericalApproximationElider]), Root[-19-112 #1+384 ((#1)^2)+3072 ((#1)^3)+4096 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["0.664", FEExpressionsNumericalApproximationElider]), Root[-779+2640 #1+5760 ((#1)^2)-25600 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.543", FEExpressionsNumericalApproximationElider]), Root[-95-160 #1+1600 ((#1)^2)+5120 ((#1)^3)+4096 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["0.477", FEExpressionsNumericalApproximationElider]), Root[-19+720 #1-6080 ((#1)^2)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.286", FEExpressionsNumericalApproximationElider]), Root[-19-112 #1+384 ((#1)^2)+3072 ((#1)^3)+4096 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["0.831", FEExpressionsNumericalApproximationElider]), Root[361-4560 #1-13440 ((#1)^2)+5120 ((#1)^3)+20480 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["0.327", FEExpressionsNumericalApproximationElider]), Root[-19-1120 #1-1920 ((#1)^2)+10240 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&(1/16) (-9-(Sqrt[5])) y+x (NumericalApproximation[Root, (RowDefault["0.528", FEExpressionsNumericalApproximationElider]), Root[-19-480 #1+6080 ((#1)^2)-20480 ((#1)^3)+20480 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["0.327", FEExpressionsNumericalApproximationElider]), Root[-19-1120 #1-1920 ((#1)^2)+10240 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&z (NumericalApproximation[Root, (RowDefault["0.159", FEExpressionsNumericalApproximationElider]), Root[-19+64 #1+896 ((#1)^2)-4096 ((#1)^3)+4096 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["0.747", FEExpressionsNumericalApproximationElider]), Root[-19+368 #1-1216 ((#1)^2)-2048 ((#1)^3)+4096 ((#1)^4)&,4], ])+y (NumericalApproximation[Root, (RowDefault["-0.543", FEExpressionsNumericalApproximationElider]), Root[-95-160 #1+1600 ((#1)^2)+5120 ((#1)^3)+4096 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.286", FEExpressionsNumericalApproximationElider]), Root[-19+112 #1+384 ((#1)^2)-3072 ((#1)^3)+4096 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["-0.327", FEExpressionsNumericalApproximationElider]), Root[-19+1120 #1-1920 ((#1)^2)-10240 ((#1)^3)+20480 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["-0.831", FEExpressionsNumericalApproximationElider]), Root[361+4560 #1-13440 ((#1)^2)-5120 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.543", FEExpressionsNumericalApproximationElider]), Root[-95+160 #1+1600 ((#1)^2)-5120 ((#1)^3)+4096 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["-0.747", FEExpressionsNumericalApproximationElider]), Root[-19-368 #1-1216 ((#1)^2)+2048 ((#1)^3)+4096 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["-0.159", FEExpressionsNumericalApproximationElider]), Root[-19-64 #1+896 ((#1)^2)+4096 ((#1)^3)+4096 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.286", FEExpressionsNumericalApproximationElider]), Root[-19+112 #1+384 ((#1)^2)-3072 ((#1)^3)+4096 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["-0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["-0.664", FEExpressionsNumericalApproximationElider]), Root[-779-2640 #1+5760 ((#1)^2)+25600 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&(1/16) (9+(Sqrt[5])) y+z (NumericalApproximation[Root, (RowDefault["-0.327", FEExpressionsNumericalApproximationElider]), Root[-19+1120 #1-1920 ((#1)^2)-10240 ((#1)^3)+20480 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["-0.528", FEExpressionsNumericalApproximationElider]), Root[-19+480 #1+6080 ((#1)^2)+20480 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.543", FEExpressionsNumericalApproximationElider]), Root[-95+160 #1+1600 ((#1)^2)-5120 ((#1)^3)+4096 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["-0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["-0.477", FEExpressionsNumericalApproximationElider]), Root[-19-720 #1-6080 ((#1)^2)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.286", FEExpressionsNumericalApproximationElider]), Root[-19-112 #1+384 ((#1)^2)+3072 ((#1)^3)+4096 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["-0.664", FEExpressionsNumericalApproximationElider]), Root[-779-2640 #1+5760 ((#1)^2)+25600 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.286", FEExpressionsNumericalApproximationElider]), Root[-19-112 #1+384 ((#1)^2)+3072 ((#1)^3)+4096 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.327", FEExpressionsNumericalApproximationElider]), Root[-19+1120 #1-1920 ((#1)^2)-10240 ((#1)^3)+20480 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["-0.831", FEExpressionsNumericalApproximationElider]), Root[361+4560 #1-13440 ((#1)^2)-5120 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.543", FEExpressionsNumericalApproximationElider]), Root[-95-160 #1+1600 ((#1)^2)+5120 ((#1)^3)+4096 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["-0.477", FEExpressionsNumericalApproximationElider]), Root[-19-720 #1-6080 ((#1)^2)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&x (NumericalApproximation[Root, (RowDefault["-0.747", FEExpressionsNumericalApproximationElider]), Root[-19-368 #1-1216 ((#1)^2)+2048 ((#1)^3)+4096 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["-0.159", FEExpressionsNumericalApproximationElider]), Root[-19-64 #1+896 ((#1)^2)+4096 ((#1)^3)+4096 ((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["-0.543", FEExpressionsNumericalApproximationElider]), Root[-95-160 #1+1600 ((#1)^2)+5120 ((#1)^3)+4096 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&(1/16) (-9-(Sqrt[5])) y+z (NumericalApproximation[Root, (RowDefault["-0.327", FEExpressionsNumericalApproximationElider]), Root[-19+1120 #1-1920 ((#1)^2)-10240 ((#1)^3)+20480 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["-0.528", FEExpressionsNumericalApproximationElider]), Root[-19+480 #1+6080 ((#1)^2)+20480 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.879", FEExpressionsNumericalApproximationElider]), Root[-95+720 #1+640 ((#1)^2)-5120 ((#1)^3)+4096 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["0.159", FEExpressionsNumericalApproximationElider]), Root[-19+64 #1+896 ((#1)^2)-4096 ((#1)^3)+4096 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.286", FEExpressionsNumericalApproximationElider]), Root[-19-112 #1+384 ((#1)^2)+3072 ((#1)^3)+4096 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.720", FEExpressionsNumericalApproximationElider]), Root[19+24 #1-416 ((#1)^2)-256 ((#1)^3)+1024 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["-0.0664", FEExpressionsNumericalApproximationElider]), Root[19+440 #1+2720 ((#1)^2)+6400 ((#1)^3)+5120 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.621", FEExpressionsNumericalApproximationElider]), Root[-19+592 #1-576 ((#1)^2)-3072 ((#1)^3)+4096 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["-0.369", FEExpressionsNumericalApproximationElider]), Root[361-5440 ((#1)^2)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.879", FEExpressionsNumericalApproximationElider]), Root[-95+720 #1+640 ((#1)^2)-5120 ((#1)^3)+4096 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["-0.0147", FEExpressionsNumericalApproximationElider]), Root[-19-1360 #1-4480 ((#1)^2)+5120 ((#1)^3)+20480 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.327", FEExpressionsNumericalApproximationElider]), Root[-19-1120 #1-1920 ((#1)^2)+10240 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.720", FEExpressionsNumericalApproximationElider]), Root[19+24 #1-416 ((#1)^2)-256 ((#1)^3)+1024 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["-0.505", FEExpressionsNumericalApproximationElider]), Root[19-680 #1-2080 ((#1)^2)+1280 ((#1)^3)+5120 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["0.327", FEExpressionsNumericalApproximationElider]), Root[-19-1120 #1-1920 ((#1)^2)+10240 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.879", FEExpressionsNumericalApproximationElider]), Root[-95+720 #1+640 ((#1)^2)-5120 ((#1)^3)+4096 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["0.286", FEExpressionsNumericalApproximationElider]), Root[-19+112 #1+384 ((#1)^2)-3072 ((#1)^3)+4096 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["-0.159", FEExpressionsNumericalApproximationElider]), Root[-19-64 #1+896 ((#1)^2)+4096 ((#1)^3)+4096 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.621", FEExpressionsNumericalApproximationElider]), Root[-19+592 #1-576 ((#1)^2)-3072 ((#1)^3)+4096 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["-0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["0.369", FEExpressionsNumericalApproximationElider]), Root[361-5440 ((#1)^2)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.720", FEExpressionsNumericalApproximationElider]), Root[19+24 #1-416 ((#1)^2)-256 ((#1)^3)+1024 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["0.0664", FEExpressionsNumericalApproximationElider]), Root[19-440 #1+2720 ((#1)^2)-6400 ((#1)^3)+5120 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["-0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.720", FEExpressionsNumericalApproximationElider]), Root[19+24 #1-416 ((#1)^2)-256 ((#1)^3)+1024 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["0.505", FEExpressionsNumericalApproximationElider]), Root[19+680 #1-2080 ((#1)^2)-1280 ((#1)^3)+5120 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["-0.327", FEExpressionsNumericalApproximationElider]), Root[-19+1120 #1-1920 ((#1)^2)-10240 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.879", FEExpressionsNumericalApproximationElider]), Root[-95+720 #1+640 ((#1)^2)-5120 ((#1)^3)+4096 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["-0.327", FEExpressionsNumericalApproximationElider]), Root[-19+1120 #1-1920 ((#1)^2)-10240 ((#1)^3)+20480 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["0.0147", FEExpressionsNumericalApproximationElider]), Root[-19+1360 #1-4480 ((#1)^2)-5120 ((#1)^3)+20480 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.879", FEExpressionsNumericalApproximationElider]), Root[-95-720 #1+640 ((#1)^2)+5120 ((#1)^3)+4096 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["-0.0147", FEExpressionsNumericalApproximationElider]), Root[-19-1360 #1-4480 ((#1)^2)+5120 ((#1)^3)+20480 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.327", FEExpressionsNumericalApproximationElider]), Root[-19-1120 #1-1920 ((#1)^2)+10240 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.621", FEExpressionsNumericalApproximationElider]), Root[-19-592 #1-576 ((#1)^2)+3072 ((#1)^3)+4096 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["-0.369", FEExpressionsNumericalApproximationElider]), Root[361-5440 ((#1)^2)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.720", FEExpressionsNumericalApproximationElider]), Root[19-24 #1-416 ((#1)^2)+256 ((#1)^3)+1024 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["-0.505", FEExpressionsNumericalApproximationElider]), Root[19-680 #1-2080 ((#1)^2)+1280 ((#1)^3)+5120 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["0.327", FEExpressionsNumericalApproximationElider]), Root[-19-1120 #1-1920 ((#1)^2)+10240 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.720", FEExpressionsNumericalApproximationElider]), Root[19-24 #1-416 ((#1)^2)+256 ((#1)^3)+1024 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["-0.0664", FEExpressionsNumericalApproximationElider]), Root[19+440 #1+2720 ((#1)^2)+6400 ((#1)^3)+5120 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&z (NumericalApproximation[Root, (RowDefault["0.159", FEExpressionsNumericalApproximationElider]), Root[-19+64 #1+896 ((#1)^2)-4096 ((#1)^3)+4096 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.286", FEExpressionsNumericalApproximationElider]), Root[-19-112 #1+384 ((#1)^2)+3072 ((#1)^3)+4096 ((#1)^4)&,2], ])+y (NumericalApproximation[Root, (RowDefault["-0.879", FEExpressionsNumericalApproximationElider]), Root[-95-720 #1+640 ((#1)^2)+5120 ((#1)^3)+4096 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.879", FEExpressionsNumericalApproximationElider]), Root[-95-720 #1+640 ((#1)^2)+5120 ((#1)^3)+4096 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["-0.327", FEExpressionsNumericalApproximationElider]), Root[-19+1120 #1-1920 ((#1)^2)-10240 ((#1)^3)+20480 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["0.0147", FEExpressionsNumericalApproximationElider]), Root[-19+1360 #1-4480 ((#1)^2)-5120 ((#1)^3)+20480 ((#1)^4)&,2], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.720", FEExpressionsNumericalApproximationElider]), Root[19-24 #1-416 ((#1)^2)+256 ((#1)^3)+1024 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["0.505", FEExpressionsNumericalApproximationElider]), Root[19+680 #1-2080 ((#1)^2)-1280 ((#1)^3)+5120 ((#1)^4)&,4], ])+z (NumericalApproximation[Root, (RowDefault["-0.327", FEExpressionsNumericalApproximationElider]), Root[-19+1120 #1-1920 ((#1)^2)-10240 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.621", FEExpressionsNumericalApproximationElider]), Root[-19-592 #1-576 ((#1)^2)+3072 ((#1)^3)+4096 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["-0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["0.369", FEExpressionsNumericalApproximationElider]), Root[361-5440 ((#1)^2)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&x (NumericalApproximation[Root, (RowDefault["0.286", FEExpressionsNumericalApproximationElider]), Root[-19+112 #1+384 ((#1)^2)-3072 ((#1)^3)+4096 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["-0.159", FEExpressionsNumericalApproximationElider]), Root[-19-64 #1+896 ((#1)^2)+4096 ((#1)^3)+4096 ((#1)^4)&,3], ])+y (NumericalApproximation[Root, (RowDefault["-0.879", FEExpressionsNumericalApproximationElider]), Root[-95-720 #1+640 ((#1)^2)+5120 ((#1)^3)+4096 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.720", FEExpressionsNumericalApproximationElider]), Root[19-24 #1-416 ((#1)^2)+256 ((#1)^3)+1024 ((#1)^4)&,1], ])+x (NumericalApproximation[Root, (RowDefault["0.0664", FEExpressionsNumericalApproximationElider]), Root[19-440 #1+2720 ((#1)^2)-6400 ((#1)^3)+5120 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["-0.597", FEExpressionsNumericalApproximationElider]), Root[361-8320 ((#1)^2)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.62", FEExpressionsNumericalApproximationElider]), Root[1805-27840 #1-57600 ((#1)^2)+81920 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.652", FEExpressionsNumericalApproximationElider]), Root[361-3392 #1+10624 ((#1)^2)-12288 ((#1)^3)+4096 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["0.898", FEExpressionsNumericalApproximationElider]), Root[361+4160 #1-3200 ((#1)^2)-20480 ((#1)^3)+20480 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["0.212", FEExpressionsNumericalApproximationElider]), Root[361+1280 #1-23680 ((#1)^2)+40960 ((#1)^3)+20480 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.652", FEExpressionsNumericalApproximationElider]), Root[361-3392 #1+10624 ((#1)^2)-12288 ((#1)^3)+4096 ((#1)^4)&,3], ])+z (NumericalApproximation[Root, (RowDefault["-0.212", FEExpressionsNumericalApproximationElider]), Root[361-1280 #1-23680 ((#1)^2)-40960 ((#1)^3)+20480 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["0.898", FEExpressionsNumericalApproximationElider]), Root[361+4160 #1-3200 ((#1)^2)-20480 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.652", FEExpressionsNumericalApproximationElider]), Root[361+3392 #1+10624 ((#1)^2)+12288 ((#1)^3)+4096 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["0.898", FEExpressionsNumericalApproximationElider]), Root[361+4160 #1-3200 ((#1)^2)-20480 ((#1)^3)+20480 ((#1)^4)&,4], ])+x (NumericalApproximation[Root, (RowDefault["0.212", FEExpressionsNumericalApproximationElider]), Root[361+1280 #1-23680 ((#1)^2)+40960 ((#1)^3)+20480 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.652", FEExpressionsNumericalApproximationElider]), Root[361+3392 #1+10624 ((#1)^2)+12288 ((#1)^3)+4096 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.212", FEExpressionsNumericalApproximationElider]), Root[361-1280 #1-23680 ((#1)^2)-40960 ((#1)^3)+20480 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["0.898", FEExpressionsNumericalApproximationElider]), Root[361+4160 #1-3200 ((#1)^2)-20480 ((#1)^3)+20480 ((#1)^4)&,4], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.652", FEExpressionsNumericalApproximationElider]), Root[361-3392 #1+10624 ((#1)^2)-12288 ((#1)^3)+4096 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["-0.898", FEExpressionsNumericalApproximationElider]), Root[361-4160 #1-3200 ((#1)^2)+20480 ((#1)^3)+20480 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["0.212", FEExpressionsNumericalApproximationElider]), Root[361+1280 #1-23680 ((#1)^2)+40960 ((#1)^3)+20480 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["0.652", FEExpressionsNumericalApproximationElider]), Root[361-3392 #1+10624 ((#1)^2)-12288 ((#1)^3)+4096 ((#1)^4)&,3], ])+x (NumericalApproximation[Root, (RowDefault["-0.212", FEExpressionsNumericalApproximationElider]), Root[361-1280 #1-23680 ((#1)^2)-40960 ((#1)^3)+20480 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.898", FEExpressionsNumericalApproximationElider]), Root[361-4160 #1-3200 ((#1)^2)+20480 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.652", FEExpressionsNumericalApproximationElider]), Root[361+3392 #1+10624 ((#1)^2)+12288 ((#1)^3)+4096 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.898", FEExpressionsNumericalApproximationElider]), Root[361-4160 #1-3200 ((#1)^2)+20480 ((#1)^3)+20480 ((#1)^4)&,1], ])+z (NumericalApproximation[Root, (RowDefault["0.212", FEExpressionsNumericalApproximationElider]), Root[361+1280 #1-23680 ((#1)^2)+40960 ((#1)^3)+20480 ((#1)^4)&,3], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0&&y (NumericalApproximation[Root, (RowDefault["-0.652", FEExpressionsNumericalApproximationElider]), Root[361+3392 #1+10624 ((#1)^2)+12288 ((#1)^3)+4096 ((#1)^4)&,2], ])+x (NumericalApproximation[Root, (RowDefault["-0.212", FEExpressionsNumericalApproximationElider]), Root[361-1280 #1-23680 ((#1)^2)-40960 ((#1)^3)+20480 ((#1)^4)&,2], ])+z (NumericalApproximation[Root, (RowDefault["-0.898", FEExpressionsNumericalApproximationElider]), Root[361-4160 #1-3200 ((#1)^2)+20480 ((#1)^3)+20480 ((#1)^4)&,1], ])+(NumericalApproximation[Root, (RowDefault["-1.95", FEExpressionsNumericalApproximationElider]), Root[-6859-92576 #1+56576 ((#1)^2)+180224 ((#1)^3)+65536 ((#1)^4)&,1], ])≤0;

FullSimplify[ineq]//Timing

SimplePolyhedron

SimplePolyhedronQ[p]

Skeleton

PolyhedronData[pname,"Skeleton"]

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

SurfaceArea

PolyhedronData[pname,"SurfaceArea"]

RootReduce[%]

SurfaceArea[p]//RootReduce//Timing

Total[Area/@PolyhedronData[pname,"Polygons"]]//RootReduce//Timing

VertexCount

PolyhedronData[pname,"VertexCount"]

VertexSubsetHulls

hulls=PolyhedronData[pname,"VertexSubsetHulls"]

v=PolyhedronData[pname,"Vertices"];

g1=Graphics3D[{{Opacity[.5],{Yellow,p}},{Red,ConvexHullMesh[v[[Lookup[hulls,"Icosahedron"][[1]]]]]}},Boxed->False,Method->{"ShrinkWrap"->True},ImageSize->Small]

g2=Graphics3D[{{Opacity[.3],{Yellow,p}},{Red,ConvexHullMesh[v[[Lookup[hulls,"Icosidodecahedron"][[1]]]]]}},Boxed->False,Method->{"ShrinkWrap"->True},ImageSize->Small]

g3=Graphics3D[{{Opacity[.4],{Yellow,p}},Transpose[{{Red,Blue,Green,Purple,White},ConvexHullMesh[v[[#]]]&/@Lookup[hulls,"Octahedron"]}]},Boxed->False,Method->{"ShrinkWrap"->True},ImageSize->Small]

PolyhedronData["OctahedronFiveCompound"]

GraphicsRow[{g1,g2,g3}]

Platonic

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

Volume

PolyhedronData[pname,"Volume"]

Volume[p]//ToAlgebraicRoot//FullSimplify

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

(Canonical) "PentakisIcosidodecahedron" construction

Cooey

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

C0=Sqrt[5 (5-2 Sqrt[5])]/5;
C1=Sqrt[10 (5-Sqrt[5])]/10;
C2=(6 Sqrt[5]+Sqrt[2 (85-Sqrt[5])]-16)/19;
C3=Sqrt[10 (5+Sqrt[5])]/10;
C4=(7-5 Sqrt[5]+Sqrt[2 (125+41 Sqrt[5])])/19;
C5=Sqrt[10 (5-Sqrt[5])]/5;

V0={0,0,C5};
V1={0,0,-C5};
V2={C5,0,0};
V3={-C5,0,0};
V4={0,C5,0};
V5={0,-C5,0};
V6={C2,0,C4};
V7={C2,0,-C4};
V8={-C2,0,C4};
V9={-C2,0,-C4};
V10={C4,C2,0};
V11={C4,-C2,0};
V12={-C4,C2,0};
V13={-C4,-C2,0};
V14={0,C4,C2};
V15={0,C4,-C2};
V16={0,-C4,C2};
V17={0,-C4,-C2};
V18={C0,C1,C3};
V19={C0,C1,-C3};
V20={C0,-C1,C3};
V21={C0,-C1,-C3};
V22={-C0,C1,C3};
V23={-C0,C1,-C3};
V24={-C0,-C1,C3};
V25={-C0,-C1,-C3};
V26={C3,C0,C1};
V27={C3,C0,-C1};
V28={C3,-C0,C1};
V29={C3,-C0,-C1};
V30={-C3,C0,C1};
V31={-C3,C0,-C1};
V32={-C3,-C0,C1};
V33={-C3,-C0,-C1};
V34={C1,C3,C0};
V35={C1,C3,-C0};
V36={C1,-C3,C0};
V37={C1,-C3,-C0};
V38={-C1,C3,C0};
V39={-C1,C3,-C0};
V40={-C1,-C3,C0};
V41={-C1,-C3,-C0};

vertices=Symbol/@Table["V"<>ToString[n],{n,0,41}]

faces=Sort[1+{{6,0,20},{6,20,28},{6,28,26},{6,26,18},{6,18,0},{7,1,19},{7,19,27},{7,27,29},{7,29,21},{7,21,1},{8,0,22},{8,22,30},{8,30,32},{8,32,24},{8,24,0},{9,1,25},{9,25,33},{9,33,31},{9,31,23},{9,23,1},{10,2,27},{10,27,35},{10,35,34},{10,34,26},{10,26,2},{11,2,28},{11,28,36},{11,36,37},{11,37,29},{11,29,2},{12,3,30},{12,30,38},{12,38,39},{12,39,31},{12,31,3},{13,3,33},{13,33,41},{13,41,40},{13,40,32},{13,32,3},{14,4,38},{14,38,22},{14,22,18},{14,18,34},{14,34,4},{15,4,35},{15,35,19},{15,19,23},{15,23,39},{15,39,4},{16,5,36},{16,36,20},{16,20,24},{16,24,40},{16,40,5},{17,5,41},{17,41,25},{17,25,21},{17,21,37},{17,37,5},{0,18,22},{0,24,20},{1,21,25},{1,23,19},{2,26,28},{2,29,27},{3,31,33},{3,32,30},{4,34,35},{4,39,38},{5,37,36},{5,40,41},{18,26,34},{19,35,27},{20,36,28},{21,29,37},{22,38,30},{23,31,39},{24,32,40},{25,41,33}}];

p=Polyhedron[vertices,faces]

p=Polyhedron[];

SortBy[Union@SimplifyNumericallyDistinct[PolyhedronEdgeLengths[p]],N]

N[%]

<<MathWorld`Polyhedra`

Midsphere[p//N,Method->"PointLineDistance"]

{PolyhedronData["CanonicalChamferedDodecahedron"],Graphics3D[p]}

cham=PolyhedronData["CanonicalChamferedDodecahedron","Polyhedron"]/.Polyhedron[v_,f_]:>Polyhedron[v/PolyhedronData["CanonicalChamferedDodecahedron","Midradius"],f];

rot=RotationMatrix[{vertices[[7]],{0,0,1}}]//RootReduce

penticos=Polyhedron[rot.#&/@vertices,faces]

Graphics3D[{Opacity[.5],{Red,penticos},{Green,cham},{Yellow,Sphere[]}},Boxed->False]

vertices2=rot.#&/@vertices//FullSimplify

p=Polyhedron[vertices2,faces]

Extend midpoints

Graphics3D[{PolyhedronData["CanonicalChamferedDodecahedron","Polyhedron"],MapIndexed[Text[#2[[1]],#,Background->White]&,v=PolyhedronData["CanonicalChamferedDodecahedron","Vertices"]]},Boxed->False]

PolyhedronData["CanonicalChamferedDodecahedron","EdgeLengths"]//N

hex1={51,52,63,71,77,67};
hex2={52,37,38,53,58,63};

h1=Mean[v[[hex1]]]//RootReduce

h2=Mean[v[[hex2]]]//RootReduce

Mean[v[[{52,63}]]]

Solve[#,a]&/@%

FindCanonicalPolyhedron

poly=PolyhedronData["CanonicalChamferedDodecahedron","Polyhedron"]/.Polyhedron[v_,f_]:>Polyhedron[v/PolyhedronData["CanonicalChamferedDodecahedron","Midradius"],f]

Graphics3D[
{Opacity[.5],Blue,dual=DualPolyhedron[poly]/.Polyhedron[v_,f_]:>Polyhedron[1.09v,f],Red,poly},Boxed->False]

(can=FindCanonicalPolyhedron[dual,WorkingPrecision->100,MaxIterations->5000,PrecisionGoal->20,"ProgressInterval"->500,"TangentFactor"->1/10,"PlanarFactor"->1/10,Debug->True])//Timing

Graphics3D[can]

SimplePolyhedronQ[dual]

Graphics3D[{Opacity[.5],{Red,can},{Green,poly},{Yellow,Sphere[]}},Boxed->False]

PolyhedronData["CanonicalChamferedDodecahedron"]

(can2=FindCanonicalPolyhedron[can,WorkingPrecision->200,MaxIterations->10000,PrecisionGoal->100,"ProgressInterval"->1000,"TangentFactor"->1/10,"PlanarFactor"->1/10,Debug->True])//Timing

can2=Polyhedron[];

<<MathWorld`Graphs`

(can3=FindCanonicalPolyhedron[can2,WorkingPrecision->200,MaxIterations->100000,PrecisionGoal->50,"ProgressInterval"->1000,"TangentFactor"->1/10,"PlanarFactor"->1/10,Debug->True])//Timing

(can4=FindCanonicalPolyhedron[can3,WorkingPrecision->200,MaxIterations->100000,PrecisionGoal->110,"ProgressInterval"->1000,"TangentFactor"->1/10,"PlanarFactor"->1/10,Debug->True])//Timing

can4=Polyhedron[];

(can5=FindCanonicalPolyhedron[can4,WorkingPrecision->300,MaxIterations->100000,PrecisionGoal->205,"ProgressInterval"->1000,"TangentFactor"->1/10,"PlanarFactor"->1/10,Debug->True])//Timing

(can6=FindCanonicalPolyhedron[N[can5,1000],WorkingPrecision->500,MaxIterations->200000,PrecisionGoal->305,"ProgressInterval"->5000,"TangentFactor"->1/10,"PlanarFactor"->1/10,Debug->True])//Timing

Graphics3D[{Opacity[.5],{Red,can5},{Green,poly},{Yellow,Sphere[]}},Boxed->False]

v=PolyhedronCoordinates[poly];

tip=Mean[v[[poly[[2,1]]]]]//FullSimplify

vv=can5[[1]];

vv[[1]]

Mean[vv]

Position[Chop[vv],_?(Count[#,0]==2&)]//Flatten

vv[[{3,12,26,31}]]//N

v0=vv[[3]]

rot=RotationMatrix[{v0-Mean[vv],{0,0,-1}}]

vvv=rot.(#-Mean[vv])&/@vv;

vvv[[{3,12,26,31}]]

Map[ToAlgebraicRoot[#,WorkingPrecision->150]&,vvv,{2}]

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

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

v=PolyhedronCoordinates[Polyhedron[]];

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[Polyhedron[]],Boxed->False]//Quiet

(Canonical) "PentakisIcosidodecahedron" net construction

Graphics3D[{PolyhedronData["PentakisIcosidodecahedron","Polyhedron"],MapIndexed[Text[#2[[1]],#,Background->White]&,v=PolyhedronData["PentakisIcosidodecahedron","Vertices"]]},Boxed->False]

eqtri={21,37,29};
isostri={17,37,21};

EuclideanDistance@@@Partition[v[[eqtri]],2,1,1]//Quiet//FullSimplify//Union

N[%]

EuclideanDistance@@@Partition[v[[isostri]],2,1,1]//Quiet//FullSimplify

N[%]

PolygonAngle[Polygon[v[[eqtri]]]]//Quiet//Timing

ArcCos[ToAlgebraicRoot/@Cos[PolygonAngle[Polygon[v[[eqtri]]]]]]//FullSimplify

Total[%]-Pi//FullSimplify

N[%]

N[{ArcCos[(1/8) (2+(Sqrt[5])-2 (Sqrt[5-2 (Sqrt[5])]))],ArcCos[(1/8) (3-(Sqrt[5])+(Sqrt[2 (5+(Sqrt[5]))]))],ArcCos[(1/8) (3-(Sqrt[5])+(Sqrt[2 (5+(Sqrt[5]))]))]}]

α=ArcCos[(1/8) (2+(Sqrt[5])-2 (Sqrt[5-2 (Sqrt[5])]))];
β=ArcCos[(1/8) (3-(Sqrt[5])+(Sqrt[2 (5+(Sqrt[5]))]))];
a=(1/4) (3-(Sqrt[5])+(Sqrt[2 (5+(Sqrt[5]))]));

v=Join[{{0,0}},Table[Through[{Cos,Sin}[α/2+i α]],{i,-3,2}]]//N[#,10000]&;
v=Join[v,{v[[4]]+RotationMatrix[-Pi/3].(v[[5]]-v[[4]])}];
v=Join[v,SimilarityTransform[v,{{3,4},{5,8}},Range[8]]];
v=Join[v,SimilarityTransform[v,{{3,2},{12,16}},Range[8]]];
v=Join[v,{v[[11]]+RotationMatrix[Pi/3].(v[[10]]-v[[11]])}];
v=Join[v,SimilarityTransform[v,{{4,8},{14,13}},Range[8]]];
v=Join[v,SimilarityTransform[v,{{5,8},{28,29}},Range[8]]];
v=Join[v,{v[[36]]+RotationMatrix[Pi/3].(v[[35]]-v[[36]]),v[[38]]+RotationMatrix[Pi/3].(v[[27]]-v[[38]])}];
v=Join[v,SimilarityTransform[v,{{3,4},{30,33}},Range[7]]];
v=Join[v,{v[[48]]+RotationMatrix[-Pi/3].(v[[49]]-v[[48]])}];
v=Join[v,SimilarityTransform[v,{{8,4},{46,31}},Range[8]]];
v=Join[v,{v[[54]]+RotationMatrix[Pi/3].(v[[53]]-v[[54]]),v[[56]]+RotationMatrix[-Pi/3].(v[[57]]-v[[56]]),v[[55]]+RotationMatrix[Pi/3].(v[[54]]-v[[55]])}];
v=Join[v,SimilarityTransform[v,{{3,4},{62,54}},Range[7]]];
v=Join[v,{v[[69]]+RotationMatrix[Pi/3].(v[[68]]-v[[69]]),v[[57]]+RotationMatrix[-Pi/3].(v[[58]]-v[[57]])}];
v=Join[v,SimilarityTransform[v,{{6,7},{58,71}},Range[7]]];
v=Join[v,{v[[76]]+RotationMatrix[Pi/3].(v[[75]]-v[[76]]),v[[75]]+RotationMatrix[Pi/3].(v[[74]]-v[[75]]),v[[74]]+RotationMatrix[Pi/3].(v[[73]]-v[[74]])}];
v=Join[v,SimilarityTransform[v,{{11,6},{81,73}},Range[8]]];
v=Join[v,SimilarityTransform[v,{{2,3},{79,75}},Range[8]]];
v=Join[v,SimilarityTransform[v,{{11,6},{97,93}},Range[7]]];

f={{1,4,5},{1,5,6},{1,6,7},{1,2,3},{1,3,4},{4,8,5}};
f=Join[f,f+8,f+16,{{10,25,11}}];
f=Join[f,25+Take[f,6],33+Take[f,6],{{35,42,36},{27,43,38}},43+Take[f,5],{{49,48,51}}];
f=Join[f,Take[f,6]+51,{{57,56,61},{53,60,54},{54,62,55}}];
f=Join[f,Take[f,5]+62,{{69,68,70},{71,58,57}}];
f=Join[f,Take[f,5]+71,{{75,79,76},{80,75,74},{74,73,81}}];
f=Join[f,Take[f,6]+81];
f=Join[f,Take[f,6]+89];
f=Join[f,Take[f,5]+97];

EuclideanDistance@@v[[{5,6}]]//FullSimplify

N[%]

Graphics[{FaceForm[LightYellow],EdgeForm[Black],Polygon[v,f],MapIndexed[Text[#2[[1]],#,Background->White]&,v]}]

Total[Area[Polygon[v,#]]&/@f]

PolyhedronData["PentakisIcosidodecahedron","SurfaceArea"]

N[%]

vexact=Map[ToAlgebraicRoot[#,WorkingPrecision->2000]&,v,{2}];//Timing

Position[vexact,_?InexactNumberQ]

Length[vexact]

ToAlgebraicRoot[vexact[[96,1]],WorkingPrecision->5000]//Timing

vexact2=ReplacePart[vexact,{96,1}->(NumericalApproximation[Root, (RowDefault["6.99", FEExpressionsNumericalApproximationElider]), Root[204923564808851989740912316564386645375549797256617922424007721368745118820386801-7225554613139672433666372216487996506747433352248381156829015882281223258359463936 ((#1)^2)+32738390957208328955465986991931036032516598988146346655249266955903383146827087872 ((#1)^4)-51996923598312651041212527571468425712605100250682966407219949194064157645071187968 ((#1)^6)+«1»-9634352228553148182504097474199526748343665177488404626051622902578143734867689472 ((#1)^10)+613234498771391462929087110296224560213444688008058034483639084634632984683610112 ((#1)^12)-14466655756099000173726780047006211745930993272061965048108115484350453817278464 ((#1)^14)+115792089237316195423570985008687907853269984665640564039457584007913129639936 ((#1)^16)&,16], ])];

Position[vexact2,_?InexactNumberQ]

vexact2-v

ToAlgebraicRoot@Total[Area[Polygon[vexact2,#]]&/@f]

PolyhedronData["PentakisIcosidodecahedron","SurfaceArea"]

vfinal=Union[vexact2];

ffinal=Sort[vexact2[[#]]&/@f/.Thread[vfinal->Range[Length[vfinal]]]]

vfinal//FullSimplify

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

ToAlgebraicRoot@Total[Area[Polygon[vfinal,#]]&/@ffinal]

Perspective projections

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

Manipulate[PolyhedronProjectionGraph[N@PolyhedronData["PentakisIcosidodecahedron","Polyhedron"],{a,b,c}],{a,-1,1},{b,-1,1},{c,-1.2,1.2}]

{-.975,-1,-1.03}

g0=PolyhedronProjectionGraph[PolyhedronData["PentakisIcosidodecahedron","Polyhedron"],{-.975,-1,-1.03}]

{1, 0, 0}

g0=PolyhedronProjectionGraph[PolyhedronData["PentakisIcosidodecahedron","Polyhedron"],{1,.001,0}]

v=GraphEmbedding[PolyhedronProjectionGraph[PolyhedronData["PentakisIcosidodecahedron","Polyhedron"],{1,z,0}]]//.Abs[z_]^2:>z^2//FullSimplify

v2=Limit[v,z->0,Direction->"FromAbove"]//FullSimplify

Annotate[g0,VertexCoordinates->v2]

{0, 1, 0}

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

{0, 0, 1}

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

{0, 1, 1}

g0=PolyhedronProjectionGraph[PolyhedronData["PentakisIcosidodecahedron","Polyhedron"],{0,1,1}]

{1, 1, 0}

g0=PolyhedronProjectionGraph[PolyhedronData["PentakisIcosidodecahedron","Polyhedron"],{1,1,0}]

{1, 0, 1}

g0=PolyhedronProjectionGraph[PolyhedronData["PentakisIcosidodecahedron","Polyhedron"],{1,0,1}]

{1, 1, 1}

g0=PolyhedronProjectionGraph[PolyhedronData["PentakisIcosidodecahedron","Polyhedron"],{1,1,1}]

PolyhedronData

PolyhedronDataString

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

WriteString[file,PolyhedronDataString[p,
"StandardName"->"PentakisIcosidodecahedron",
"Name"->"canonical pentakis icosidodecahedron",
"Information"->"CanonicaPentakisIcosidodecahedron",
"Classes"->{"Canonical"},
"Dual"->"CanonicalChamferedDodecahedron"
]]

Close[file]