Compound of two great icosahedra
Appearance
Compound of two great icosahedra | |
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Type | Uniform compound |
Index | UC52 |
Polyhedra | 2 great icosahedra |
Faces | 16+24 triangles |
Edges | 60 |
Vertices | 24 |
Symmetry group | octahedral (Oh) |
Subgroup restricting to one constituent | pyritohedral (Th) |
![](http://upload.wikimedia.org/wikipedia/commons/thumb/d/de/Compound_of_two_great_icosahedra.stl/220px-Compound_of_two_great_icosahedra.stl.png)
In geometry, the compound of two great icosahedra is a uniform polyhedron compound. It's composed of 2 great icosahedra, in the same arrangement as in the compound of 2 icosahedra.
The triangles in this compound decompose into two orbits under action of the symmetry group: 16 of the triangles lie in coplanar pairs in octahedral planes, while the other 24 lie in unique planes.
The great icosahedron, as a uniform retrosnub tetrahedron , is similar to these snub-pair compounds: compound of two icosahedra, compound of two snub cubes and compound of two snub dodecahedra.
References
[edit]- Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra", Mathematical Proceedings of the Cambridge Philosophical Society, 79 (3): 447–457, doi:10.1017/S0305004100052440, MR 0397554.