Compound of three square antiprisms

Compound of three square antiprisms
TypeUniform compound
IndexUC42
Polyhedra3 square antiprisms
Faces24 triangles,
6 squares
Edges48
Vertices24
Symmetry groupchiral octahedral (O)
Subgroup restricting to one constituent4-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