Great Dodecahedron-Small Stellated Dodecahedron Compound

Author

Eric W. Weisstein
September 20, 2023

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Polyhedra/GreatDodecahedron-SmallStellatedDodecahedronCompound.nb.

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

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

Construction

Dual

pname="GreatDodecahedron";

dname=PolyhedronData[pname,"Dual","Name"]

PolyhedronData[pname,"Dual","Scale"]

midrs={PolyhedronData[pname,"Midradius"],PolyhedronData[dname,"Midradius"]}

Divide@@midrs//FullSimplify

N[%]

GoldenRatio^2.

GraphicsRow[With[{
s={Yellow,PolyhedronData[pname,"Midsphere"]},
style=Directive[Black,Italic,FontFamily->"Times",14]
},
{
Graphics3D[{s,Green,Opacity[.5],PolyhedronData[pname,"Polyhedron"]},Boxed->False,PlotLabel->TextCell[Style[PolyhedronData[pname,"Name"],style],PageWidth->200,TextAlignment->Center]],
Graphics3D[{s,Red,Opacity[.3],PolyhedronData[pname,"Dual","Polyhedron"]},Boxed->False,PlotLabel->Style[PolyhedronData[dname,"Name"],style]],
Graphics3D[{
{Green,Opacity[.5],PolyhedronData[pname,"Polyhedron"]},
{Red,Opacity[.3],PolyhedronData[pname,"Dual","Polyhedron"]},
s
},Boxed->False,PlotLabel->Style["compound with midsphere",style]],
Graphics3D[{
PolyhedronData[pname,"Polyhedron"],
PolyhedronData[pname,"Dual","Polyhedron"]
},Boxed->False,PlotLabel->Style["compound",style]]
}],Alignment->Top,ImageSize->800]