For the sake of beauty, at the expense of time.
The main goal is to compute the Great Snub Icosidodecahedron from scratch, and make all intersection lines visible. The Great Snub Icosidodecahedron has (20+60) triangles and 12 pentagrams and is a nonconvex uniform polyhedron, indexed as U57. https://en.wikipedia.org/wiki/Great_snub_icosidodecahedron
Card Boards:
In[]:=
Framed[Grid[{{Graphics[triangle[CirclePoints[3]]],Graphics[triangleII[CirclePoints[3]]],Graphics[pentagram[CirclePoints[5][[{1,3,5,2,4}]]]]}}],Background->LightBlue]
Out[]=
Chiral Card Boards:
In[]:=
Framed[Grid[{{Graphics[Scale[triangle[CirclePoints[3]],{-1,1},{0,0}]],Graphics[Scale[triangleII[CirclePoints[3]],{-1,1},{0,0}]],Graphics[Scale[pentagram[CirclePoints[5][[{1,3,5,2,4}]]],{-1,1},{0,0}]]}}],Background->LightCyan]
Out[]=
The Great Snub Icosidodecahedron (face view on a red pentagram):
In[]:=
Framed[snub=Graphics3D[greatsnubicosidodecahedron={{{Red,Map[pentagram[U57vc[[#]]//N]&,s5]}},{Blue,Map[triangle[U57vc[[#]]//N]&,s31]},{White,Map[triangleII[U57vc[[#]]//N]&,s32]}},BoxedFalse,Lighting->"Neutral",ViewProjection"Orthographic",ViewPointMean[U57vc[[{13,42,27,51,18}]]],ViewVerticalMean[U57vc[[{32}]]]],Background->LightBlue]
Out[]=
Shaded gray:
In[]:=
snub/.RGBColor[___]White
Out[]=
Outlined:
In[]:=
Show[snub/.RGBColor[___]White,Lighting{{"Ambient",White}}]
Out[]=
Edgeview (on an edge of the convex hull):
In[]:=
Show[snub,BoxedFalse,Lighting->"Neutral",ViewProjection"Orthographic",ViewPointMean[U57vc[[{13,24}]]],ViewVerticalMean[U57vc[[{14,21,44}]]]]
Out[]=
Faceview of a blue triangle:
In[]:=
Show[snub,BoxedFalse,Lighting->"Neutral",ViewProjection"Orthographic",ViewPointMean[U57vc[[{1,24,42}]]],ViewVerticalU57vc[[6]]]
Out[]=
Chiral Great Snub Icosidodecahedron (face view on a red pentagram):

CITE THIS NOTEBOOK

Great snub icosidodecahedron U57​
by Oliver Seipel​
Wolfram Community, STAFF PICKS, July 24, 2023
​https://community.wolfram.com/groups/-/m/t/2974665