Octagonal-great enneagrammic duoprism
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Octagonal-great enneagrammic duoprism | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Ogstedip |
Coxeter diagram | x8o2x9/4o () |
Elements | |
Cells | 9 octagonal prisms, 8 great enneagrammic prisms |
Faces | 72 squares, 9 octagons, 8 great enneagrams |
Edges | 72+72 |
Vertices | 72 |
Vertex figure | Digonal disphenoid, edge lengths √2+√2 (base 1), 2cos(4π/9) (base 2), √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Gistep–9/4–gistep: 135° |
Op–4–gistep: 90° | |
Op–8–op: 20° | |
Central density | 4 |
Number of external pieces | 26 |
Level of complexity | 12 |
Related polytopes | |
Army | Semi-uniform oedip |
Regiment | Ogstedip |
Dual | Octagonal-great enneagrammic duotegum |
Conjugates | Octagonal-enneagonal duoprism, Octagonal-enneagrammic duoprism, Octagrammic-enneagonal duoprism, Octagrammic-enneagrammic duoprism, Octagrammic-great enneagrammic duoprism |
Abstract & topological properties | |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | I2(8)×I2(9), order 288 |
Convex | No |
Nature | Tame |
The octagonal-great enneagrammic duoprism, also known as ogstedip or the 8-9/4 duoprism, is a uniform duoprism that consists of 9 octagonal prisms and 8 great enneagrammic prisms, with 2 of each at each vertex.
Vertex coordinates[edit | edit source]
The coordinates of an octagonal-great enneagrammic duoprism, centered at the origin and with edge length 2sin(4π/9), are given by:
- ,
- ,
- ,
- ,
- ,
- ,
where j = 2, 4, 8.
Representations[edit | edit source]
An octagonal-great enneagrammic duoprism has the following Coxeter diagrams:
- x8o2x9/4o () (full symmetry)
- x4x2x9/4o () (BC2×I2(9) symmetry, octagons as ditetragons)
External links[edit | edit source]
- Bowers, Jonathan. "Category A: Duoprisms".
- Klitzing, Richard. "nd-mb-dip".