Octagonal-octahedral duoprism
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Octagonal-octahedral duoprism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Owoct |
Coxeter diagram | x8o o4o3x () |
Elements | |
Tera | 8 octahedral prisms, 8 triangular-octagonal duoprisms |
Cells | 64 triangular prisms, 8 octahedra, 12 octagonal prisms |
Faces | 64 triangles, 96 squares, 6 octagons |
Edges | 48+96 |
Vertices | 48 |
Vertex figure | Square scalene, edge lengths 1 (base square), √2+√2 (top), √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Ope–oct–ope: 135° |
Todip–op–todip: | |
Todip–trip–ope: 90° | |
Central density | 1 |
Number of external pieces | 16 |
Level of complexity | 10 |
Related polytopes | |
Army | Owoct |
Regiment | Owoct |
Dual | Octagonal-cubic duotegum |
Conjugate | Octagrammic-octahedral duoprism |
Abstract & topological properties | |
Flag count | 7680 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | B3×I2(8), order 768 |
Convex | Yes |
Nature | Tame |
The octagonal-octahedral duoprism or owoct is a convex uniform duoprism that consists of 8 octahedral prisms and 8 triangular-octagonal duoprisms. Each vertex joins 2 octahedral prisms and 4 triangular-octagonal duoprisms.
Vertex coordinates[edit | edit source]
The vertices of an octagonal-octahedral duoprism of edge length 1 are given by all permutations and sign changes of the last three coordinates of:
- ,
- .
Representations[edit | edit source]
An octagonal-octahedral duoprism has the following Coxeter diagrams:
- x8o o4o3x () (full symmetry)
- x4x o4o3x () (octagons as ditetragons)
- x8o o3x3o () (octahedra as tetratetrahedra)
- x4x o3x3o () (octagons as ditetragons and octahedra as tetratetrahedra)
- xo3ox xx8oo&#x (triangular-octagonal duoprism atop triangle-gyrated triangular-octagonal duoprism)
External links[edit | edit source]
- Klitzing, Richard. "owoct".