Compound of twenty octahedra
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Short description: Polyhedral compound
 | This article relies largely or entirely on a single source. (August 2025) |
| Compound of twenty octahedra | |
|---|---|
| 280px | |
| Type | Uniform compound |
| Index | UC14 |
| Polyhedra | 20 octahedra |
| Faces | 40+120 triangles |
| Edges | 240 |
| Vertices | 60 |
| Symmetry group | icosahedral (Ih) |
| Subgroup restricting to one constituent | 6-fold improper rotation (S6) |
The compound of twenty octahedra is a uniform polyhedron compound. It's composed of a symmetric arrangement of 20 octahedra (considered as triangular antiprisms). It is a special case of the compound of 20 octahedra with rotational freedom, in which pairs of octahedral vertices coincide.[1]
Related polyhedra
This compound shares its edge arrangement with the great dirhombicosidodecahedron, the great disnub dirhombidodecahedron, and the compound of twenty tetrahemihexahedra.
It may be constructed as the exclusive or of the two enantiomorphs of the great snub dodecicosidodecahedron.
| 100px Convex hull (Non-uniform Rhombicosidodecahedron) |
100px Great snub dodecicosidodecahedron |
100px Great dirhombicosidodecahedron |
| 100px Great disnub dirhombidodecahedron |
100px Compound of twenty octahedra |
100px Compound of twenty tetrahemihexahedra |
See also
- Compound of three octahedra
- Compound of four octahedra
- Compound of five octahedra
- Compound of ten octahedra
References
- ↑ Skilling, J. (May 1976). "Uniform compounds of uniform polyhedra" (in en). Mathematical Proceedings of the Cambridge Philosophical Society 79 (3): 447–457. doi:10.1017/S0305004100052440. ISSN 0305-0041. https://www.cambridge.org/core/product/identifier/S0305004100052440/type/journal_article.
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