Compound of four triangular prisms

Compound of four triangular prisms
Type	Uniform compound
Index	UC30
Polyhedra	4 triangular prisms
Faces	8 triangles, 12 squares
Edges	36
Vertices	24
Symmetry group	chiral octahedral (O)
Subgroup restricting to one constituent	3-fold dihedral (D3)

This uniform polyhedron compound is a chiral symmetric arrangement of 4 triangular prisms, aligned with the axes of three-fold rotational symmetry of an octahedron.

Cartesian coordinates

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

(±1, ±(1+√2), ±(1−√2))

with an even number of minuses in the '±' choices, together with all the odd permutations with an odd number of minuses in the '±' choices.

References

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