Jump to content

Compound of great icosahedron and great stellated dodecahedron

From Wikipedia, the free encyclopedia
(Redirected from Wenninger model index 61)
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.

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.
[edit]