Truncated dodecahedral prism | |
---|---|
![]() Schlegel diagram Decagonal prisms hidden | |
Type | Prismatic uniform polychoron |
Uniform index | 60 |
Schläfli symbol | t0,1,3{3,5,2} or t{3,5}×{} |
Coxeter-Dynkin | ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Cells | 34 total: 2 t0,1{5,3} 12 {}x{10} 20 {}x{3} |
Faces | 154 total: 40 {3} 90 {4} 24 {10} |
Edges | 240 |
Vertices | 120 |
Vertex figure | ![]() Isosceles-triangular pyramid |
Symmetry group | [5,3,2], order 240 |
Properties | convex |
In geometry, a truncated dodecahedral 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.
In geometry, the grand 600-cell or grand polytetrahedron is a regular star 4-polytope with Schläfli symbol {3,3,5/2}. It is one of 10 regular Schläfli-Hess polytopes. It is the only one with 600 cells.
In geometry, the small stellated 120-cell or stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol {5/2,5,3}. It is one of 10 regular Schläfli-Hess polytopes.
In geometry, the icosahedral 120-cell, polyicosahedron, faceted 600-cell or icosaplex is a regular star 4-polytope with Schläfli symbol {3,5,5/2}. It is one of 10 regular Schläfli-Hess polytopes.
In geometry, the grand 120-cell or grand polydodecahedron is a regular star 4-polytope with Schläfli symbol {5,3,5/2}. It is one of 10 regular Schläfli-Hess polytopes.
In geometry, the great stellated 120-cell or great stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol {5/2,3,5}. It is one of 10 regular Schläfli-Hess polytopes.
In geometry, the great icosahedral 120-cell, great polyicosahedron or great faceted 600-cell is a regular star 4-polytope with Schläfli symbol {3,5/2,5}. It is one of 10 regular Schläfli-Hess polytopes.
In geometry, the great 120-cell or great polydodecahedron is a regular star 4-polytope with Schläfli symbol {5,5/2,5}. It is one of 10 regular Schläfli-Hess polytopes. It is one of the two such polytopes that is self-dual.
In geometry, the grand stellated 120-cell or grand stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol {5/2,5,5/2}. It is one of 10 regular Schläfli-Hess polytopes. It is also one of two such polytopes that is self-dual.
In geometry, a cuboctahedral prism is a convex uniform 4-polytope. This 4-polytope has 16 polyhedral cells: 2 cuboctahedra connected by 8 triangular prisms and 6 cubes.
In geometry, a truncated tetrahedral prism is a convex uniform polychoron. This polychoron has 10 polyhedral cells: 2 truncated tetrahedra connected by 4 triangular prisms and 4 hexagonal prisms. It has 24 faces: 8 triangular, 18 square, and 8 hexagons. It has 48 edges and 24 vertices.
In geometry, an icosahedral prism is a convex uniform 4-polytope. This 4-polytope has 22 polyhedral cells: 2 icosahedra connected by 20 triangular prisms. It has 70 faces: 30 squares and 40 triangles. It has 72 edges and 24 vertices.
In 4-dimensional geometry, a truncated octahedral prism or omnitruncated tetrahedral prism is a convex uniform 4-polytope. This 4-polytope has 16 cells It has 64 faces, and 96 edges and 48 vertices.
In geometry, an icosidodecahedral prism is a convex uniform polychoron.
In geometry, a rhombicosidodecahedral prism or small rhombicosidodecahedral prism is a convex uniform polychoron.
In geometry, a truncated cubic prism is a convex uniform polychoron.
In geometry, a snub cubic prism or snub cuboctahedral prism is a convex uniform polychoron.
In geometry, a truncated icosahedral prism is a convex uniform polychoron.
In geometry, a truncated icosidodecahedral prism or great rhombicosidodecahedral prism is a convex uniform 4-polytope.
In geometry, a snub dodecahedral prism or snub icosidodecahedral prism is a convex uniform polychoron.
In geometry of 4 dimensions, a 3-6 duoprism, a duoprism and 4-polytope resulting from the Cartesian product of a triangle and a hexagon.