Enneagonal-hexagonal antiprismatic duoprism |
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Rank | 5 |
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Type | Uniform |
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Notation |
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Bowers style acronym | Ehap |
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Coxeter diagram | x9o s2s12o () |
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Elements |
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Tera | 9 hexagonal antiprismatic prisms, 12 triangular-enneagonal duoprisms, 2 hexagonal-enneagonal duoprisms |
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Cells | 108 triangular prisms, 18 hexagonal prisms, 9 hexagonal antiprisms, 12+12 enneagonal prisms |
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Faces | 108 triangles, 108+108 squares, 18 hexagons, 12 enneagons |
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Edges | 108+108+108 |
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Vertices | 108 |
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Vertex figure | Isosceles-trapezoidal scalene, edge lengths 1, 1, 1, √3 (base trapezoid), 2cos(π/9) (top), √2 (side 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 | Tedip–ep–tedip: = |
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| Happip–hap–happip: 140° |
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| Tedip–ep–hendip: = |
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| Tedip–trip–happip: 90° |
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| Hendip–hip–happip: 90° |
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Height | |
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Central density | 1 |
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Number of external pieces | 23 |
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Level of complexity | 40 |
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Related polytopes |
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Army | Ehap |
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Regiment | Ehap |
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Dual | Enneagonal-hexagonal antitegmatic duotegum |
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Conjugates | Enneagrammic-hexagonal antiprismatic duoprism, Great enneagrammic-hexagonal antiprismatic duoprism |
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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(9)×I2(12)×A1+, order 432 |
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Convex | Yes |
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Nature | Tame |
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The enneagonal-hexagonal antiprismatic duoprism or ehap is a convex uniform duoprism that consists of 9 hexagonal antiprismatic prisms, 2 hexagonal-enneagonal duoprisms, and 12 triangular-enneagonal duoprisms. Each vertex joins 2 hexagonal antiprismatic prisms, 3 triangular-enneagonal duoprisms, and 1 hexagonal-enneagonal duoprism.
The vertices of an enneagonal-hexagonal antiprismatic duoprism of edge length 2sin(π/9) are given by:
where j = 2, 4, 8.
An enneagonal-hexagonal antiprismatic duoprism has the following Coxeter diagrams:
- x9o s2s12o () (full symmetry; hexagonal antiprisms as alternated dodecagonal prisms)
- x9o s2s6s () (hexagonal antiprisms as alternated dihexagonal prisms)