Compound of great icosahedron and great stellated dodecahedron

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Compound of great icosahedron and stellated dodecahedron
Compound of great icosahedron and stellated dodecahedron.png
Type stellation and compound
Coxeter diagram CDel node 1.pngCDel 5-2.pngCDel node.pngCDel 3.pngCDel node.pngCDel node.pngCDel 5-2.pngCDel node.pngCDel 3.pngCDel node 1.png
Convex hull Dodecahedron
Polyhedra1 great icosahedron
1 great stellated dodecahedron
Faces20 triangles
12 pentagrams
Edges60
Vertices32
Symmetry group icosahedral (Ih)

There are two different compounds of great icosahedron and great stellated dodecahedron: one is a dual compound and a stellation of the great icosidodecahedron, the other is a stellation of the icosidodecahedron.

Contents

Dual compound

It can be seen as a polyhedron compound of a great icosahedron and great stellated dodecahedron. It is one of five compounds constructed from a Platonic solid or Kepler-Poinsot solid, and its dual. It is a stellation of the great icosidodecahedron.

It has icosahedral symmetry (Ih) and it has the same vertex arrangement as a great rhombic triacontahedron.

This can be seen as one of the two three-dimensional equivalents of the compound of two pentagrams ({10/4} "decagram"); this series continues into the fourth dimension as compounds of star 4-polytopes.

Skeleton pair Gr20 and dual, Petrie, stick, size s.png
Skeleton pair Gr20 and dual, Petrie, stick, size s, 5-fold.png
Petrie decagrams of both solids

Stellation of the icosidodecahedron

This polyhedron is a stellation of the icosidodecahedron, and given as Wenninger model index 61. It has the same vertex arrangement as a rhombic triacontahedron, its convex hull.

Second compound stellation of icosidecahedron.png

The stellation facets for construction are:

Second compound stellation of icosidecahedron facets.png
Facets from triangle
Second compound stellation of icosidecahedron pentfacets.png
Facets from pentagon

See also

References