| bgcolor=#e7dcc3 colspan=2 | Compound of two snub cubes | |
|---|---|---|
| align=center colspan=2 | ||
| Type | Uniform compound | |
| Index | UC68 | |
| Schläfli symbol | βr | |
| Coxeter diagram | ||
| Polyhedra | 2 snub cubes | |
| Faces | 16+48 triangles 12 squares | |
| Edges | 120 | |
| Vertices | 48 | |
| Symmetry group | octahedral (Oh) | |
| Subgroup restricting to one constituent | chiral octahedral (O) |
The vertex arrangement of this compound is shared by a convex nonuniform truncated cuboctahedron, having rectangular faces, alongside irregular hexagons and octagons, each alternating with two edge lengths.
Together with its convex hull, it represents the snub cube-first projection of the nonuniform snub cubic antiprism.
Cartesian coordinates for the vertices are all the permutations of
(±1, ±ξ, ±1/ξ)
where ξ is the real solution to
\xi3+\xi2+\xi=1,
which can be written
\xi=
| 1 | |
| 3 |
\left(\sqrt[3]{17+3\sqrt{33}}-\sqrt[3]{-17+3\sqrt{33}}-1\right)
or approximately 0.543689. ξ is the reciprocal of the tribonacci constant.
Equally, the tribonacci constant, t, just like the snub cube, can compute the coordinates as:
(±1, ±t, ±)
This compound can be seen as the union of the two chiral alternations of a truncated cuboctahedron: