Dodecahedral hyperprism

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Dodecahedral hyperprism
Orthographic projection (12 of 24 pentagons colored)
Type	Prismatic uniform polychoron
Cells	2 (5.5.5) 12 (4.4.5)
Faces	30 24
Edges	80
Vertices	40
Vertex configuration	Equilateral-triangular pyramid
Symmetry group	[5,3]x[]
Schläfli symbol	x
Properties	convex

In geometry, a dodecahedral hyperprism is a convex uniform polychoron (four dimensional polytope). This polychoron 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.

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.

The picture shows an edge map of this polychoron, and has half of the pentagonal faces colored to show the two dodecahedra. The dodecahedra are regular, but look flattened because of the projection and direction of viewing.

Alternative names:

1. Dodecahedral dyadic prism Norman W. Johnson
2. Dope (for dodecahedral prism) Jonathan Bowers
3. Dodecahedral prism

It is one of 18 convex uniform hyperprisms created by using uniform prisms to connect pairs of parallel Platonic solids or Archimedean solids.

External links

• [Figure 57] Prismatic convex uniform polychora (George Olshevsky)

 

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