Compound of three square antiprisms

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Compound of three square antiprisms
UC42-3 square antiprisms.png
Type Uniform compound
Index UC42
Polyhedra 3 square antiprisms
Faces 24 triangles,
6 squares
Edges 48
Vertices 24
Symmetry group chiral octahedral (O)
Subgroup restricting to one constituent 4-fold dihedral (D4)

This uniform polyhedron compound is a symmetric arrangement of 3 square antiprisms, aligned with the three axes of 4-fold rotational symmetry of a cube.

Cartesian coordinates[edit]

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

(±√(√2+1), ±√(√2−1), ±1)

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 (03): 447–457, doi:10.1017/S0305004100052440, MR 0397554 .