Pentagonal retroprism
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| Pentagonal retroprism | |
|---|---|
 | |
| Rank | 3 |
| Type | Isogonal |
| Space | Spherical |
| Elements | |
| Faces | 10 isosceles triangles, 2 pentagons |
| Edges | 10+10 |
| Vertices | 10 |
| Vertex figure | Crossed isosceles trapezoid |
| Related polytopes | |
| Army | Pip |
| Regiment | * |
| Dual | Pentagonal concave antitegum |
| Conjugate | Pentagrammic antiprism |
| Abstract & topological properties | |
| Euler characteristic | 2 |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | H2×A1, order 20 |
| Convex | No |
| Nature | Tame |
The pentagonal retroprism, also called the pentagonal crossed antiprism, is a prismatic isogonal polyhedron. It consists of 2 base pentagons and 10 isosceles triangles. Each vertex joins one pentagon and three triangles. It is a crossed antiprism based on a pentagon, seen as a 5/4-gon rather than 5/1. It cannot be made uniform.
It is isomorphic to the pentagonal antiprism.
In vertex figures[edit | edit source]
Pentagonal retroprisms appear as vertex figures of four uniform polychora: the small pentagonal retroprismatoverted dishecatonicosachoron, great pentagonal retroprismatoverted dishecatonicosachoron, pentagonal retroprismatoverted hexacosihecatonicosachoron, and quasiprismatohecatonicosachoron.
External links[edit | edit source]
- Klitzing, Richard. "n/d-ap".