bgcolor=#e7dcc3 colspan=2 | Compounds of ten octahedra | |
---|---|---|
align=center colspan=2 | ||
Type | Uniform compound | |
Index | UC15 and UC16 | |
Polyhedra | 10 octahedra | |
Faces | 20+60 triangles | |
Edges | 120 | |
Vertices | 60 | |
Symmetry group | icosahedral (Ih) | |
Subgroup restricting to one constituent | 3-fold antiprismatic (D3d) |
Cartesian coordinates for the vertices of this compound are all the cyclic permutations of
(0, ±(τ-1 + 2sτ), ±(τ - 2sτ-1))
(±(- sτ2), ±(+ s(2τ - 1)), ±(+ sτ-2))
(±(τ-1 - sτ), ±(τ + sτ-1), ±3s)
where τ = (1 +)/2 is the golden ratio (sometimes written φ) and s is either +1 or -1. Setting s = -1 gives UC15, while s = +1 gives UC16.