Compound of three square antiprisms
From Wikipedia, the free encyclopedia
| 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.
[edit] 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.
[edit] References
- John Skilling, Uniform Compounds of Uniform Polyhedra, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 79, pp. 447-457, 1976.
