Decagonal-square 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 | Dasquap |
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Coxeter diagram | x10o s2s8o () |
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Elements |
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Tera | 10 square antiprismatic prisms, 8 triangular-decagonal duoprisms, 2 square-decagonal duoprisms |
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Cells | 80 triangular prisms, 20 cubes, 10 square antiprisms, 8+8 decagonal prisms |
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Faces | 80 triangles, 20+80+80 squares, 8 decagons |
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Edges | 80+80+80 |
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Vertices | 80 |
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Vertex figure | Isosceles-trapezoidal scalene, edge lengths 1, 1, 1, √2 (base trapezoid), √(5+√5)/2 (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 | Squappip–squap–squappip: 144° |
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| Tradedip–dip–tradedip: = |
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| Tradedip–dip–squadedip: = |
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| Tradedip–trip–squappip: 90° |
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| Squadedip–cube–squappip: 90° |
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Height | |
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Central density | 1 |
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Number of external pieces | 20 |
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Level of complexity | 40 |
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Related polytopes |
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Army | Dasquap |
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Regiment | Dasquap |
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Dual | Decagonal-square antitegmatic duotegum |
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Conjugate | Decagrammic-square 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(10)×I2(8)×A1+, order 320 |
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Convex | Yes |
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Nature | Tame |
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The decagonal-square antiprismatic duoprism or dasquap is a convex uniform duoprism that consists of 10 square antiprismatic prisms, 2 square-decagonal duoprisms, and 8 triangular-decagonal duoprisms. Each vertex joins 2 square antiprismatic prisms, 3 triangular-decagonal duoprisms, and 1 square-decagonal duoprism.
The vertices of a decagonal-square antiprismatic duoprism of edge length 1 are given by:
A decagonal-square antiprismatic duoprism has the following Coxeter diagrams:
- x10o s2s8o (full symmetry; square antiprisms as alternated octagonal prisms)
- x10o s2s4s () (square antiprisms as alternated ditetragonal prisms)
- x5x s2s8o () (decagons as dipentagons)
- x5x s2s4s ()