Compound of five octahemioctahedraTypeUniform compoundIndexUC61Polyhedra5 octahemioctahedraFaces40 triangles, 20 hexagonsEdges120Vertices60Symmetry groupicosahedral (Ih)Subgroup restricting to one constituentpyritohedral (Th) In geometry, this uniform polyhedron compound is a composition of 5 octahemioctahedra, in the same vertex arrangement as in the compound of 5 cuboctahedra. It could also be called an icosidisicosahedron.
Filling There is some controversy on how to colour the faces of this polyhedron compound. Although the common way to fill in a polygon is to just colour its whole interior, this can result in some filled regions hanging as membranes over empty space. Hence, the "neo filling" is sometimes used instead as a more accurate filling. In the neo filling, orientable polyhedra are filled traditionally, but non-orientable polyhedra have their faces filled with the modulo-2 method (only odd-density regions are filled in). In addition, overlapping regions of coplanar faces can cancel each other out. Usage of the "neo filling" makes the compound of five octahemioctahedra a hollow polyhedron compound.
Traditional filling"Neo filling"
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