Compound of four octahedra
(Redirected from Octahedron 4-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) |
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
[edit]Cartesian coordinates for the vertices of this compound are all the permutations of
- (±2, ±1, ±2)
See also
[edit]- Compound of three octahedra
- Compound of five octahedra
- Compound of ten octahedra
- Compound of twenty octahedra
- Compound of four cubes
References
[edit]- Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, Bibcode:1976MPCPS..79..447S, doi:10.1017/S0305004100052440, MR 0397554, S2CID 123279687.
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