Grand hendecagrammic-dodecagrammic duoprism |
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Rank | 4 |
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Type | Uniform |
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Notation |
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Coxeter diagram | x11/5o x12/5o () |
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Elements |
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Cells | 12 grand hendecagrammic prisms, 11 dodecagrammic prisms |
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Faces | 132 squares, 12 grand hendecagrams, 11 dodecagrams |
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Edges | 132+132 |
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Vertices | 132 |
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Vertex figure | Digonal disphenoid, edge lengths 2cos(5π/11) (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 | Gashenp–4–stwip: 90° |
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| Gashenp–11/5–gashenp: 30° |
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| Stwip–12/5–stwip: |
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Central density | 25 |
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Number of external pieces | 46 |
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Level of complexity | 24 |
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Related polytopes |
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Army | Semi-uniform hentwadip |
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Dual | Grand hendecagrammic-dodecagrammic duotegum |
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Conjugates | Hendecagonal-dodecagonal duoprism, Hendecagonal-dodecagrammic duoprism, Small hendecagrammic-dodecagonal duoprism, Small hendecagrammic-dodecagrammic duoprism, Hendecagrammic-dodecagonal duoprism, Hendecagrammic-dodecagrammic duoprism, Great hendecagrammic-dodecagonal duoprism, Great hendecagrammic-dodecagrammic duoprism, Grand hendecagrammic-dodecagonal duoprism |
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Abstract & topological properties |
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Flag count | 3168 |
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Euler characteristic | 0 |
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Orientable | Yes |
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Properties |
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Symmetry | I2(11)×I2(12), order 528 |
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Convex | No |
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Nature | Tame |
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The grand hendecagrammic-dodecagrammic duoprism, also known as the 11/5-12/5 duoprism, is a uniform duoprism that consists of 12 grand hendecagrammic prisms and 11 dodecagrammic prisms, with 2 of each at each vertex.
The vertex coordinates of a grand hendecagrammic-dodecagrammic duoprism, centered at the origin and with edge length 2sin(5π/11), are given by:
- ,
- ,
- ,
- ,
- ,
- ,
where j = 2, 4, 6, 8, 10.
A grand hendecagrammic-dodecagrammic duoprism has the following Coxeter diagrams: