Icosidisicosahedron

The icosidisicosahedron, iddei, or compound of five octahemioctahedra is a uniform polyhedron compound. It consists of 40 triangles (which form coplanar pairs combining into 20 hexagrams) and 20 hexagons (also pairing up into 10 stellated dodecagons), with two of each joining at a vertex.

It can be formed by replacing each cuboctahedron in the antirhombicosicosahedron with the octahemioctahedron with which it shares its edge skeleton.