Compound of great icosahedron and great stellated dodecahedron

Compound of great icosahedron and stellated dodecahedron
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.

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 (I_h) 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.

great icosahedron

great stellated dodecahedron

compound

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.

The stellation facets for construction are:

Facets from triangle

Facets from pentagon

See also

• Compound of two tetrahedra
• Compound of cube and octahedron
• Compound of dodecahedron and icosahedron
• Compound of small stellated dodecahedron and great dodecahedron

References

• Wenninger, Magnus (1974). Polyhedron Models. Cambridge University Press. ISBN 0-521-09859-9., p. 90.
• Wenninger, Magnus (1983). Dual Models. Cambridge University Press. ISBN 0-521-54325-8., pp. 51-53.
• Martyn Cundy and A. Rollett. "Great Icosahedron Plus Great Stellated Dodecahedron". §3.10.4 in Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 132-133, 1989.

External links

• Weisstein, Eric W. "Great Icosahedron-Great Stellated Dodecahedron Compound". MathWorld.
• Great Stellated Dodecahedron plus Great Icosahedron - metallic paper model
• VRML George Hart: VRML transparent model