In geometry, the truncated icosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces.
It has 30 square faces, 20 regular hexagonal faces, 12 regular decagonal faces, 120 vertices and 180 edges – more than any other convex nonprismatic uniform polyhedron. Since each of its faces has point symmetry (equivalently, 180° rotational symmetry), the truncated icosidodecahedron is a zonohedron.
Alternate interchangeable names include:
The name truncated icosidodecahedron, originally given by Johannes Kepler, is somewhat misleading. If one truncates an icosidodecahedron by cutting the corners off, one does not get this uniform figure: instead of squares the truncation has golden rectangles. However, the resulting figure is topologically equivalent to this and can always be deformed until the faces are regular.