Octagonal-hendecagonal duoprismatic prism |
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Rank | 5 |
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Type | Uniform |
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Notation |
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Bowers style acronym | Ohenip |
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Coxeter diagram | x x8o x11o |
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Elements |
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Tera | 11 square-octagonal duoprisms, 8 square-hendecagonal duoprisms, 2 octagonal-hendecagonal duoprisms |
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Cells | 88 cubes, 8+16 hendecagonal prisms, 11+22 octagonal prisms |
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Faces | 88+88+176 squares, 22 octagons, 16 hendecagons |
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Edges | 88+176+176 |
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Vertices | 176 |
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Vertex figure | Digonal disphenoidal pyramid, edge lengths √2+√2 (disphenoid base 1), 2cos(π/11) (disphenoid base 2), √2 (remaining edges) |
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Measures (edge length 1) |
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Circumradius | |
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Hypervolume | |
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Diteral angles | Sodip–op–sodip: |
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| Shendip–henp–shendip: 135° |
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| Shendip–cube–sodip: 90° |
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| Ohendip–op–sodip: 90° |
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| Shendip–henp–ohendip: 90° |
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Height | 1 |
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Central density | 1 |
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Number of external pieces | 21 |
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Level of complexity | 30 |
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Related polytopes |
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Army | Ohenip |
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Regiment | Ohenip |
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Dual | Octagonal-hendecagonal duotegmatic tegum |
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Conjugates | Octagonal-small hendecagrammic duoprismatic prism, Octagonal-hendecagrammic duoprismatic prism, Octagonal-great hendecagrammic duoprismatic prism, Octagonal-grand hendecagrammic duoprismatic prism, Octagrammic-hendecagonal duoprismatic prism, Octagrammic-small hendecagrammic duoprismatic prism, Octagrammic-hendecagrammic duoprismatic prism, Octagrammic-great hendecagrammic duoprismatic prism, Octagrammic-grand hendecagrammic duoprismatic prism |
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Abstract & topological properties |
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Euler characteristic | 2 |
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Orientable | Yes |
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Properties |
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Symmetry | I2(8)×I2(11)×A1, order 704 |
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Convex | Yes |
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Nature | Tame |
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The octagonal-hendecagonal duoprismatic prism or ohenip, also known as the octagonal-hendecagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 octagonal-hendecagonal duoprisms, 8 square-hendecagonal duoprisms, and 11 square-octagonal duoprisms. Each vertex joins 2 square-octagonal duoprisms, 2 square-hendecagonal duoprisms, and 1 octagonal-hendecagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.
The vertices of an octagonal-hendecagonal duoprismatic prism of edge length 2sin(π/11) are given by all permutations of the first two coordinates of:
where j = 2, 4, 6, 8, 10.
An octagonal-hendecagonal duoprismatic prism has the following Coxeter diagrams:
- x x8o x11o (full symmetry)
- x x4x x11o (octagons as ditetragons)
- xx8oo xx11oo&#x (octagonal-hendecagonal duoprism atop octagonal-hendecagonal duoprism)
- xx4xx xx11oo&#x