Miller's Monster: The Polyhedron with 1280 Faces to Fold
Great Dirhombicosidodecahedron ("Miller's Monster")
The Great Dirhombicosidodecahedron, known as Miller's Monster, is a uniform star polyhedron with 124 faces, 240 edges, and 60 vertices. It uniquely has eight faces meeting at each vertex and is the only uniform polyhedron with snub faces that are squares. This page documents the construction of a physical model, requiring 1280 external facelets, 42 A4 pages of nets, and an edge length of 21.6 cm.
It is the only uniform polyhedron with as many as 8 faces meeting at each vertex (two purple pentagrams, two red triangles, and four yellow squares).