Octagonal-dodecahedral duoprism
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Octagonal-dodecahedral duoprism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Odoe |
Coxeter diagram | x8o x5o3o |
Elements | |
Tera | 12 pentagonal-octagonal duoprisms, 8 dodecahedral prisms |
Cells | 96 pentagonal prisms, 30 octagonal prisms, 8 dodecahedra |
Faces | 240 squares, 96 pentagons, 20 octagons |
Edges | 160+240 |
Vertices | 160 |
Vertex figure | Triangular scalene, edge lengths (1+√5)/2 (base triangle), √2+√2 (top), √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Dope–doe–dope: 135° |
Podip–op–podip: | |
Podip–pip–dope: 90° | |
Central density | 1 |
Number of external pieces | 20 |
Level of complexity | 10 |
Related polytopes | |
Army | Odoe |
Regiment | Odoe |
Dual | Octagonal-icosahedral duotegum |
Conjugates | Octagrammic-dodecahedral duoprism, Octagonal-great stellated dodecahedral duoprism, Octagrammic-great stellated dodecahedral duoprism |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | H3×I2(8), order 1920 |
Convex | Yes |
Nature | Tame |
The octagonal-dodecahedral duoprism or odoe is a convex uniform duoprism that consists of 8 dodecahedral prisms and 12 pentagonal-octagonal duoprisms. Each vertex joins 2 dodecahedral prisms and 3 pentagonal-octagonal duoprisms.
Vertex coordinates[edit | edit source]
The vertices of an octagonal-dodecahedral duoprism of edge length 1 are given by:
as well as all even permutations of the last three coordinates of:
Representations[edit | edit source]
An octagonal-dodecahedral duoprism has the following Coxeter diagrams:
- x8o x5o3o (full symmetry)
- x4x x5o3o (octagons as ditetragons)
External links[edit | edit source]
- Klitzing, Richard. "odoe".