Prisme pentagonalIn geometry, the pentagonal prism is a prism with a pentagonal base. It is a type of heptahedron with seven faces, fifteen edges, and ten vertices. If faces are all regular, the pentagonal prism is a semiregular polyhedron, more generally, a uniform polyhedron, and the third in an infinite set of prisms formed by square sides and two regular polygon caps. It can be seen as a truncated pentagonal hosohedron, represented by Schläfli symbol t{2,5}.
Truncated cuboctahedral prismIn geometry, a truncated cuboctahedral prism or great rhombicuboctahedral prism is a convex uniform polychoron (four-dimensional polytope). It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of Platonic solids or Archimedean solids in parallel hyperplanes. Net Truncated-cuboctahedral dyadic prism (Norman W.
Truncated icosidodecahedral prismIn geometry, a truncated icosidodecahedral prism or great rhombicosidodecahedral prism is a convex uniform 4-polytope (four-dimensional polytope). It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of Platonic solids or Archimedean solids in parallel hyperplanes. Truncated icosidodecahedral dyadic prism (Norman W.
Point groups in four dimensionsIn geometry, a point group in four dimensions is an isometry group in four dimensions that leaves the origin fixed, or correspondingly, an isometry group of a 3-sphere. 1889 Édouard Goursat, Sur les substitutions orthogonales et les divisions régulières de l'espace, Annales Scientifiques de l'École Normale Supérieure, Sér. 3, 6, (pp. 9–102, pp. 80–81 tetrahedra), Goursat tetrahedron 1951, A. C. Hurley, Finite rotation groups and crystal classes in four dimensions, Proceedings of the Cambridge Philosophical Society, vol.
Tetrahedral prismIn geometry, a tetrahedral prism is a convex uniform 4-polytope. This 4-polytope has 6 polyhedral cells: 2 tetrahedra connected by 4 triangular prisms. It has 14 faces: 8 triangular and 6 square. It has 16 edges and 8 vertices. It is one of 18 uniform polyhedral prisms created by using uniform prisms to connect pairs of parallel Platonic solids and Archimedean solids. Tetrahedral dyadic prism (Norman W.
Rectified 120-cellIn geometry, a rectified 120-cell is a uniform 4-polytope formed as the rectification of the regular 120-cell. E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as tC120. There are four rectifications of the 120-cell, including the zeroth, the 120-cell itself. The birectified 120-cell is more easily seen as a rectified 600-cell, and the trirectified 120-cell is the same as the dual 600-cell. In geometry, the rectified 120-cell or rectified hecatonicosachoron is a convex uniform 4-polytope composed of 600 regular tetrahedra and 120 icosidodecahedra cells.
Cantellated 5-cellIn four-dimensional geometry, a cantellated 5-cell is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation, up to edge-planing) of the regular 5-cell. The cantellated 5-cell or small rhombated pentachoron is a uniform 4-polytope. It has 30 vertices, 90 edges, 80 faces, and 20 cells. The cells are 5 cuboctahedra, 5 octahedra, and 10 triangular prisms. Each vertex is surrounded by 2 cuboctahedra, 2 triangular prisms, and 1 octahedron; the vertex figure is a nonuniform triangular prism.
Cantellated 24-cellsIn four-dimensional geometry, a cantellated 24-cell is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation) of the regular 24-cell. There are 2 unique degrees of cantellations of the 24-cell including permutations with truncations. The cantellated 24-cell or small rhombated icositetrachoron is a uniform 4-polytope. The boundary of the cantellated 24-cell is composed of 24 truncated octahedral cells, 24 cuboctahedral cells and 96 triangular prisms.
Truncated 120-cellsIn geometry, a truncated 120-cell is a uniform 4-polytope formed as the truncation of the regular 120-cell. There are three truncations, including a bitruncation, and a tritruncation, which creates the truncated 600-cell. The truncated 120-cell or truncated hecatonicosachoron is a uniform 4-polytope, constructed by a uniform truncation of the regular 120-cell 4-polytope. It is made of 120 truncated dodecahedral and 600 tetrahedral cells. It has 3120 faces: 2400 being triangles and 720 being decagons.
Octahedral prismIn geometry, an octahedral prism is a convex uniform 4-polytope. This 4-polytope has 10 polyhedral cells: 2 octahedra connected by 8 triangular prisms. Octahedral dyadic prism (Norman W. Johnson) Ope (Jonathan Bowers, for octahedral prism) Triangular antiprismatic prism Triangular antiprismatic hyperprism It is a Hanner polytope with vertex coordinates, permuting first 3 coordinates: ([±1,0,0]; ±1) The octahedral prism consists of two octahedra connected to each other via 8 triangular prisms.
