Pentagonal-dodecahedral duoprism
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Pentagonal-dodecahedral duoprism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Pedoe |
Coxeter diagram | x5o x5o3o |
Elements | |
Tera | 12 pentagonal duoprisms, 5 dodecahedral prisms |
Cells | 30+60 pentagonal prisms, 5 dodecahedra |
Faces | 150 squares, 20+60 pentagons |
Edges | 100+150 |
Vertices | 100 |
Vertex figure | Triangular scalene, edge lengths (1+√5)/2 (base triangle and top), √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Pedip–pip–pedip: |
Dope–doe–dope: 108° | |
Pedip–pip–dope: 90° | |
Central density | 1 |
Number of external pieces | 17 |
Level of complexity | 10 |
Related polytopes | |
Army | Pedoe |
Regiment | Pedoe |
Dual | Pentagonal-icosahedral duotegum |
Conjugate | Pentagrammic-great stellated dodecahedral duoprism |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | H3×H2, order 1200 |
Convex | Yes |
Nature | Tame |
The pentagonal-dodecahedral duoprism or pedoe is a convex uniform duoprism that consists of 5 dodecahedral prisms and 12 pentagonal duoprisms. Each vertex joins 2 dodecahedral prisms and 3 pentagonal duoprisms.
Vertex coordinates[edit | edit source]
The vertices of a pentagonal-dodecahedral duoprism of edge length 1 are given by:
as well as all even permutations of the last three coordinates of:
External links[edit | edit source]
- Klitzing, Richard. "pedoe".