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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 edit

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.

 
great icosahedron
 
great stellated dodecahedron
 
compound
 
 
Petrie decagrams of both solids

Stellation of the icosidodecahedron edit

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 edit

References edit

  • 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 edit

 

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