Compound of two snub cubes

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Compound of two snub cubes
UC68-2 snub cubes.png
Type Uniform compound
Index UC68
Schläfli symbol βr{4,3}
Coxeter diagram CDel node h3.pngCDel 4.pngCDel node h3.pngCDel 3.pngCDel node h3.png
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)

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 CDel node h3.pngCDel 4.pngCDel node h3.pngCDel 3.pngCDel node h3.png.

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.

Cartesian coordinates[edit]

Cartesian coordinates for the vertices are all the permutations of

(±1, ±ξ, ±1/ξ)

where ξ is the real solution to

which can be written

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[edit]

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

Snubcubes in grCO.svg

References[edit]

  • Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79: 447–457, doi:10.1017/S0305004100052440, MR 0397554 .