Compound of three square antiprisms
| 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) |
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, MR 0397554.