Great enneagrammic-dodecagonal duoprism |
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Rank | 4 |
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Type | Uniform |
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Notation |
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Coxeter diagram | x9/4o x12o () |
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Elements |
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Cells | 12 great enneagrammic prisms, 9 dodecagonal prisms |
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Faces | 108 squares, 12 great enneagrams, 9 dodecagons |
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Edges | 108+108 |
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Vertices | 108 |
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Vertex figure | Digonal disphenoid, edge lengths 2cos(4π/9) (base 1), (√6+√2)/2 (base 2), √2 (sides) |
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Measures (edge length 1) |
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Circumradius | |
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Hypervolume | |
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Dichoral angles | Gistep–9/4–gistep: 150° |
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| Gistep–4–twip: 90° |
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| Twip–12–twip: 20° |
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Central density | 4 |
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Number of external pieces | 30 |
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Level of complexity | 12 |
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Related polytopes |
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Army | Semi-uniform etwadip |
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Dual | Great enneagrammic-dodecagonal duotegum |
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Conjugates | Enneagonal-dodecagonal duoprism, Enneagonal-dodecagrammic duoprism, Enneagrammic-dodecagonal duoprism, Enneagrammic-dodecagrammic duoprism, Great enneagrammic-dodecagrammic duoprism |
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Abstract & topological properties |
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Euler characteristic | 0 |
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Orientable | Yes |
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Properties |
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Symmetry | I2(9)×I2(12), order 432 |
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Convex | No |
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Nature | Tame |
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The great enneagrammic-dodecagonal duoprism, also known as the 9/4-12 duoprism, is a uniform duoprism that consists of 12 great enneagrammic prisms and 9 dodecagonal prisms, with 2 of each at each vertex.
The coordinates of a great enneagrammic-dodecagonal duoprism, centered at the origin and with edge length 2sin(4π/9), are given by:
where j = 2, 4, 8.
A great enneagrammic-dodecagonal duoprism has the following Coxeter diagrams: