- Compound of three square antiprisms
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Compound of three square antiprisms 
Type Uniform compound Index UC42 Polyhedra 3 square antiprisms Faces 24 triangles,
6 squaresEdges 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
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, MR0397554.
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