Compound of four triangular prisms

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.

Compound of four triangular prisms
TypeUniform compound
IndexUC30
Polyhedra4 triangular prisms
Faces8 triangles,
12 squares
Edges36
Vertices24
Symmetry groupchiral octahedral (O)
Subgroup restricting to one constituent3-fold dihedral (D3)

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.


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