Great heptagrammic-small hendecagrammic duoprism |
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Rank | 4 |
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Type | Uniform |
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Notation |
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Coxeter diagram | x7/3o x11/2o () |
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Elements |
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Cells | 11 great heptagrammic prisms, 7 small hendecagrammic prisms |
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Faces | 77 squares, 11 great heptagrams, 7 small hendecagrams |
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Edges | 77+77 |
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Vertices | 77 |
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Vertex figure | Digonal disphenoid, edge lengths 2cos(3π/7) (base 1), 2cos(2π/11) (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 | Giship–7/3–giship: |
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| Giship–4–sishenp: 90° |
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| Sishenp–11/2–sishenp: |
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Central density | 6 |
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Number of external pieces | 36 |
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Level of complexity | 24 |
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Related polytopes |
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Army | Semi-uniform hehendip |
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Dual | Great heptagrammic-small hendecagrammic duotegum |
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Conjugates | Heptagonal-hendecagonal duoprism, Heptagonal-small hendecagrammic duoprism, Heptagonal-hendecagrammic duoprism, Heptagonal-great hendecagrammic duoprism, Heptagonal-grand hendecagrammic duoprism, Heptagrammic-hendecagonal duoprism, Heptagrammic-small hendecagrammic duoprism, Heptagrammic-hendecagrammic duoprism, Heptagrammic-great hendecagrammic duoprism, Heptagrammic-grand hendecagrammic duoprism, Great heptagrammic-hendecagonal duoprism, Great heptagrammic-hendecagrammic duoprism, Great heptagrammic-great hendecagrammic duoprism, Great heptagrammic-grand hendecagrammic duoprism |
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Abstract & topological properties |
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Flag count | 1848 |
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Euler characteristic | 0 |
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Orientable | Yes |
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Properties |
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Symmetry | I2(7)×I2(11), order 308 |
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Convex | No |
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Nature | Tame |
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The great heptagrammic-small hendecagrammic duoprism, also known as the 7/3-11/2 duoprism, is a uniform duoprism that consists of 11 great heptagrammic prisms and 7 small hendecagrammic prisms, with 2 of each at each vertex.
The coordinates of a great heptagrammic-small hendecagrammic duoprism, centered at the origin and with edge length 4sin(3π/7)sin(2π/11), are given by:
- ,
- ,
- ,
- ,
where j = 2, 4, 6 and k = 2, 4, 6, 8, 10.