Compound of three square antiprisms

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.

Compound of three square antiprisms
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)

Cartesian coordinates

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.

References

• 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.