Compound of four octahedra
From HandWiki
Short description: Polyhedral compound
| Compound of four octahedra | |
|---|---|
| |
| Type | Uniform compound |
| Index | UC12 |
| Convex hull | Nonuniform truncated cube |
| Polyhedra | 4 octahedra |
| Faces | 8+24 triangles |
| Edges | 48 |
| Vertices | 24 |
| Symmetry group | octahedral (Oh) |
| Subgroup restricting to one constituent | 3-fold antiprismatic (D3d) |
File:Compound of four octahedra.stl The compound of four octahedra is a uniform polyhedron compound. It's composed of a symmetric arrangement of 4 octahedra, considered as triangular antiprisms. It can be constructed by superimposing four identical octahedra, and then rotating each by 60 degrees about a separate axis (that passes through the centres of two opposite octahedral faces).
Its dual is the compound of four cubes.
Cartesian coordinates
Cartesian coordinates for the vertices of this compound are all the permutations of
- (±2, ±1, ±2)
See also
- Compound of three octahedra
- Compound of five octahedra
- Compound of ten octahedra
- Compound of twenty octahedra
- Compound of four cubes
References
- Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society 79 (3): 447–457, doi:10.1017/S0305004100052440, Bibcode: 1976MPCPS..79..447S.
 |  |
