Many famous and not-so-famous polyhedra appear amidst slightly advanced geometrical topics. Here are some examples:

Great Dirhombicosidodecahedron An Imbedding of the Hyperbolic Plane Octahemioctahedron A Finite Projective Space The Six-Dimensional Cube Two Models of the Real Projective Plane How to Make the Mathieu Group M(24) The Dodecadodecahedron and the Golay Code The Regular Polyhedra (of index two) Models made from Balls and Straws Another View of Gosset's Figure Van Oss Projection of the 600-Cell

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