Compound of two snub cubes
# Compound of two snub cubes

Compound of two snub cubes :

| Type | Uniform compound |
| - | - |
| Index | $UC_{68}$ |
| Schläfli symbol | βr{4,3} |
| Coxeter diagram | |
| Polyhedra | 2 snub cubes |
| Faces | 16+48 triangles 12 squares |
| Edges | 120 |
| Vertices | 48 |
| Symmetry group | octahedral $(O_h)$ |
| Subgroup restricting to one constituent | chiral octahedral (O) |

This uniform polyhedron compound is a composition of the 2 enantiomers of the snub cube. As a holosnub, it is represented by Schläfli symbol βr{4,3} and Coxeter diagram .

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

Cartesian coordinates for the vertices are all the permutations of

    (±1, ±ξ, ±1/ξ)

where ξ is the real solution to

    $\xi ^{3}+\xi ^{2}+\xi =1,\,$

which can be written

    $\xi ={\frac {1}{3}}\left({\sqrt[{3}]{17+3{\sqrt {33}}}}-{\sqrt[{3}]{-17+3{\sqrt {33}}}}-1\right)$

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, ±1/t)

## Truncated cuboctahedron

This compound can be seen as the union of the two chiral alternations of a truncated cuboctahedron:

    A geometric construction of the Tribonacci constant (AC), with compass and marked ruler, according to the method described by Xerardo Neira.
