Truncated Dodecadodecahedron

In geometry, the truncated dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U59. It is given a Schläfli symbol t0,1,2{5/3,5}. It has 120 vertices and 54 faces: 30 squares, 12 decagons, and 12 decagrams. The central region of the polyhedron is connected to the exterior via 20 small triangular holes.

The name truncated dodecadodecahedron is somewhat misleading: truncation of the dodecadodecahedron would produce rectangular faces rather than squares, and the pentagram faces of the dodecahedron would turn into truncated pentagrams rather than decagrams. However, it is the quasitruncation of the dodecadodecahedron, as defined by Coxeter, Longuet-Higgins & Miller (1954). For this reason, it is also known as the quasitruncated dodecadodecahedron. Coxeter et al. credit its discovery to a paper published in 1881 by Austrian mathematician Johann Pitsch.

Read more about Truncated Dodecadodecahedron:  Cartesian Coordinates, As A Cayley Graph, See Also