Compound of four hexagonal prisms

This uniform polyhedron compound is a symmetric arrangement of 4 hexagonal prisms, aligned with the axes of threefold rotational symmetry of an octahedron. It shares the same vertex arrangement as a nonuniform rhombicuboctahedron.

Compound of four hexagonal prisms
Type	Uniform compound
Index	UC38
Polyhedra	4 hexagonal prisms
Faces	8 hexagons, 24 squares
Edges	72
Vertices	48
Symmetry group	octahedral (Oh)
Subgroup restricting to one constituent	3-fold antiprismatic (D3d)

Cartesian coordinates

Cartesian coordinates for the vertices of this compound are all the permutations of

(±1, ±(1−√6), ±(1+√6))

References

• Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, doi:10.1017/S0305004100052440, MR 0397554.