Compound of two icosahedraTypeUniform compoundIndexUC46Schläfli symbolsβ{3,4}βr{3,3}Coxeter diagramsPolyhedra2 icosahedraFaces16+24 trianglesEdges60Vertices24Symmetry groupoctahedral (Oh)Subgroup restricting to one constituentpyritohedral (Th)
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 .
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.
Cartesian coordinates 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).
Compound of two dodecahedra The dual compound has two dodecahedra as pyritohedra in dual positions:
See also Compound of two snub cubes Compound of two snub dodecahedra
References .