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