Compound of four triangular prisms

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Compound of four triangular prisms
UC30-4 triangular prisms.png
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[edit]

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.


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