Compound of two icosahedra
This uniform polyhedron compound is a composition of 2 icosahedra. It has octahedral symmetry Oh. As a holosnub, it is represented by Schläfli symbol β{3,4} and Coxeter diagram .
| Compound of two icosahedra | |
|---|---|
| Type | Uniform compound |
| Index | UC46 |
| Schläfli symbols | β{3,4} βr{3,3} |
| Coxeter diagrams | |
| Polyhedra | 2 icosahedra |
| Faces | 16+24 triangles |
| Edges | 60 |
| Vertices | 24 |
| Symmetry group | octahedral (Oh) |
| Subgroup restricting to one constituent | pyritohedral (Th) |
The triangles in this compound decompose into two orbits under action of the symmetry group: 16 of the triangles lie in coplanar pairs in octahedral planes, while the other 24 lie in unique planes.
It shares the same vertex arrangement as a nonuniform truncated octahedron, having irregular hexagons alternating with long and short edges.
Nonuniform and uniform truncated octahedra. The first shares its vertex arrangement with this compound. |
The icosahedron, as a uniform snub tetrahedron, is similar to these snub-pair compounds: compound of two snub cubes and compound of two snub dodecahedra.
Together with its convex hull, it represents the icosahedron-first projection of the nonuniform snub tetrahedral antiprism.