compound of great icosahedron and great stellated dodecahedron
Compound of great icosahedron and great stellated dodecahedron GudangMovies21 Rebahinxxi LK21
There are two different compounds of great" target="_blank">great icosahedron and great" target="_blank">great stellated dodecahedron: one is a dual compound and a stellation of the great" target="_blank">great icosidodecahedron, the other is a stellation of the icosidodecahedron.
Dual compound
It can be seen as a polyhedron compound of a great" target="_blank">great icosahedron and great" target="_blank">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" target="_blank">great icosidodecahedron.
It has icosahedral symmetry (Ih) and it has the same vertex arrangement as a great" target="_blank">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.
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:
See also
Compound of two tetrahedra
Compound of cube and octahedron
Compound of dodecahedron and icosahedron
Compound of small stellated dodecahedron and great" target="_blank">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" target="_blank">Great Icosahedron Plus great" target="_blank">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" target="_blank">Great Icosahedron-great" target="_blank">Great Stellated Dodecahedron Compound". MathWorld.
great" target="_blank">Great Stellated Dodecahedron plus great" target="_blank">Great Icosahedron - metallic paper model
VRML George Hart: VRML transparent model