bgcolor=#e7dcc3 colspan=2 | Compound of two icosahedra | |
---|---|---|
align=center colspan=2 | ||
Type | Uniform compound | |
Index | UC46 | |
bgcolor=#e7dcc3 width=150 | Schläfli symbols | β βr |
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.
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.
Cartesian coordinates for the vertices of this compound are all the permutations of
(±1, 0, ±τ)
where τ = (1+)/2 is the golden ratio (sometimes written φ).
The dual compound has two dodecahedra as pyritohedra in dual positions: