- Compound of two icosahedra
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Compound of two icosahedra 
Type Uniform compound Index UC46 Polyhedra 2 icosahedra Faces 16+24 triangles Edges 60 Vertices 24 Symmetry group octahedral (Oh) Subgroup restricting to one constituent pyritohedral (Th) This uniform polyhedron compound is a composition of 2 icosahedra. It has octahedral symmetry Oh.
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.Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the permutations of
- (±1, 0, ±τ)
where τ = (1+√5)/2 is the golden ratio (sometimes written φ).
References
- Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society 79 (3): 447–457, doi:10.1017/S0305004100052440, MR0397554.
External links
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