Dodecahedral prism
From Wikipedia, the free encyclopedia
In geometry, a dodecahedral prism is a convex uniform 4-polytope. This 4-polytope has 14 polyhedral cells: 2 dodecahedra connected by 12 pentagonal prisms. It has 54 faces: 30 squares and 24 pentagons. It has 80 edges and 40 vertices.
Dodecahedral prism | |
---|---|
Schlegel diagram Only one dodecahedral cell shown | |
Type | Prismatic uniform 4-polytope |
Uniform index | 57 |
Schläfli symbol | t{2,5,3} or {5,3}×{} |
Coxeter-Dynkin | |
Cells | 2 (5.5.5) 12 (4.4.5) |
Faces | 30 {4} 24 {5} |
Edges | 80 |
Vertices | 40 |
Vertex figure | Equilateral-triangular pyramid |
Dual | Icosahedral bipyramid |
Symmetry group | [5,3,2], order 240 |
Properties | convex |
It can be constructed by creating two coinciding dodecahedra in 3-space, and translating each copy in opposite perpendicular directions in 4-space until their separation equals their edge length.
It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of parallel Platonic solids or Archimedean solids.