Descriptive Geometry: Edmund Hess 1878 Great Icosidodecahedron

Great Icosidodecahedron

Reference https://en.wikipedia.org/wiki/Icosidodecahedron
https://en.wikipedia.org/wiki/Great_icosidodecahedron
https://en.wikipedia.org/wiki/Edmund_Hess
https://de.wikipedia.org/wiki/Edmund_Hess
The great icosidodecahedron is a nonconvex uniform polyhedron, indexed as U54 with Schläfli symbol r{3,5/2}. It is a rectification of the great icosahedron. It was first discovered by Edmund Hess (1843-1903; 1878). It’s build out of 12 pentagrams and 20 triangles and has the same vertices as the Icosidodecahedron:
The aim is a construction from scratch of the great Icosidodecahedron with visible edges and standardized points of view.
Mathematica code
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The Icosidodecahedron as the convex hull of the great icosidodecahedron:

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Graphics3D[{Map[Polygon[vertices[[#]]]&,{{5,9,26,22,24},{24,28,19,11,17},{11,15,27,23,13},{23,21,25,7,3},{7,14,18,9,1},{13,3,1,5,17},{22,30,10,6,28},{6,2,4,15,19},{4,8,29,21,27},{29,16,12,14,25},{8,2,10,20,16},{12,20,30,26,18}}],FaceForm[Red,Yellow],Map[Polygon[vertices[[#]]]&,{{1,3,7},{7,25,14},{14,12,18},{18,26,9},{1,9,5},{5,24,17},{13,17,11},{3,13,23},{23,27,21},{21,29,25},{29,8,16},{12,16,20},{30,20,10},{26,30,22},{24,22,28},{10,2,6},{2,8,4},{4,27,15},{15,11,19},{6,19,28}}]},ViewProjection"Orthographic",BoxedFalse,Lighting"Neutral",ViewPoint{0,-3,1.4},ViewVertical{0.2,-0.2,1}]
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The great icosidodecahedron in orthogonal projection:

Mathematica code:
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The Polyhedron
In[]:=
greaticosidodecahedron=Graphics3D[{FaceForm[Yellow,Red],Map[pentagram[vertices[[#]]]&,pentagramfaces],FaceForm[Yellow,White],Map[triangle[vertices[[#]]]&,trianglefaces]},BoxedFalse,ViewProjection"Orthographic",Lighting"Neutral",ViewPoint{0,-3,1.4},ViewVertical{0.2,-0.2,1}]
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Pentagram Face View:

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Show[greaticosidodecahedron,ViewPoint2Mean[vertices[[{29,13,14,27,1}]]],ViewVertical-Mean[vertices[[{2,4,8}]]],Lighting"Neutral"]
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%/.{RGBColor[___]White}
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Show[%,Lighting{{"Ambient",White}}]
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Triangle Face View:

In[]:=
Show[greaticosidodecahedron,ViewPoint2Mean[vertices[[{1,3,7}]]],ViewVertical-Mean[vertices[[{11,13,23,27,15}]]]]
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Edge View:

Vertex View:

Variation (Hess-Seipel-Polyhedron:)

The Polyhedron

Pentagram Face View:

Triangle Face View:

Edge View:

Vertex View: