| bgcolor=#e7dcc3 colspan=2 | Compound of great icosahedron and stellated dodecahedron | |
|---|---|---|
| align=center colspan=2 | ||
| Type | stellation and compound | |
| Coxeter diagram | ∪ | |
| Convex hull | Dodecahedron | |
| Polyhedra | 1 great icosahedron 1 great stellated dodecahedron | |
| Faces | 20 triangles 12 pentagrams | |
| Edges | 60 | |
| Vertices | 32 | |
| 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.
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 ("decagram"); this series continues into the fourth dimension as compounds of star 4-polytopes.
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.
The stellation facets for construction are:
. Magnus Wenninger . Polyhedron Models . Cambridge University Press . 1974 . 0-521-09859-9 ., p. 90.
. Magnus Wenninger . Dual Models . Cambridge University Press . 1983 . 0-521-54325-8 ., pp. 51-53.