Compound of two great icosahedra

In geometry, the compound of two great icosahedra is a uniform polyhedron compound. It is composed of 2 great icosahedra, in the same arrangement as in the compound of 2 icosahedra.

Compound of two great icosahedra
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)

3D model of a compound of two great 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

• 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.