Cantellated 120-cell

In four-dimensional geometry, a cantellated 120-cell is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation) of the regular 120-cell. There are four degrees of cantellations of the 120-cell including with permutations truncations. Two are expressed relative to the dual 600-cell. The cantellated 120-cell is a uniform 4-polytope. It is named by its construction as a Cantellation operation applied to the regular 120-cell. It contains 1920 cells, including 120 rhombicosidodecahedra, 1200 triangular prisms, 600 octahedra. Its vertex figure is a wedge, with two rhombicosidodecahedra, two triangular prisms, and one octahedron meeting at each vertex. Cantellated 120-cell Norman Johnson Cantellated hecatonicosachoron / Cantellated dodecacontachoron / Cantellated polydodecahedron Small rhombated hecatonicosachoron (Acronym srahi) (George Olshevsky and Jonathan Bowers) Ambo-02 polydodecahedron (John Conway) The cantitruncated 120-cell is a uniform polychoron. This 4-polytope is related to the regular 120-cell. The cantitruncation operation create new truncated tetrahedral cells at the vertices, and triangular prisms at the edges. The original dodecahedron cells are cantitruncated into great rhombicosidodecahedron cells. The image shows the 4-polytope drawn as a Schlegel diagram which projects the 4-dimensional figure into 3-space, distorting the sizes of the cells. In addition, the decagonal faces are hidden, allowing us to see the elemented projected inside. Cantitruncated 120-cell Norman Johnson Cantitruncated hecatonicosachoron / Cantitruncated polydodecahedron Great rhombated hecatonicosachoron (Acronym grahi) (George Olshevsky and Jonthan Bowers) Ambo-012 polydodecahedron (John Conway) The cantellated 600-cell is a uniform 4-polytope. It has 1440 cells: 120 icosidodecahedra, 600 cuboctahedra, and 720 pentagonal prisms. Its vertex figure is an isosceles triangular prism, defined by one icosidodecahedron, two cuboctahedra, and two pentagonal prisms.