# Polyhedron Category 5: Omnitruncates

Here are the 7 omnitruncates. The first two are convex and therefore are part of the Archimedean solids. Omnitruncates have the maximum number of congruent vertices for their symmetry, 48 for cubics (girco, quitco, and cotco) and 120 for doics (others). All of these are orientable. They all also show up as cells in the uniform polychora. The polychoron categories most similar to this one are 8, 9, and more distantly 10 and 14.  57. Girco - (GIR co) great rhombicuboctahedron, or rhombitruncated cuboctahedron. Symbol is xx'x. Faces are 6 octagons, 8 hexagons, and 12 squares.

58. Grid - (GRID) great icosidodecahedron, or rhombitruncatedicosidodecahedron. Symbol is xx^x. Faces are 12 decagons, 20 hexagons, and 30 squares.  59. Quitco - (QUIT co) quasitruncated cuboctahedron. Symbol is xx"x. Faces are 6 octagrams, 8 hexagons, and 12 squares.

60. Quitdid - (QUIT did) quasitruncated dodecadodecahedron. Symbol is x^x*'x. Faces are 12 decagrams, 12 decagons, and 30 squares. 61. Gaquatid - (GA qua tid) great quasitruncated icosidodecahedron. Symbol is xx*'x. Faces are 12 decagrams, 20 hexagons, and 30 squares.  62. Cotco - (COT co) cuboctitruncated cuboctahedron. Symbol is (x'x"x). Faces are 6 octagrams, 6 octagons, and 8 hexagons.

63. Idtid - (ID tid) icosidodecatruncated icosidodecahedron. Symbol is (x^x*'x). Faces are 12 decagrams, 12 decagons, and 20 hexagons.

Conjugate Pairs: girco-quitco, grid-gaquatid.

Self Conjugates: quitdid, cotco, idtid.