Hexagonal-square antiprismatic duoprism
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Hexagonal-square antiprismatic duoprism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Hasquap |
Coxeter diagram | x6o s2s8o |
Elements | |
Tera | 6 square antiprismatic prisms, 8 triangular-hexagonal duoprisms, 2 square-hexagonal duoprisms |
Cells | 48 triangular prisms, 12 cubes, 6 square antiprisms, 8+8 hexagonal prisms |
Faces | 48 triangles, 12+48+48 squares, 8 hexagons |
Edges | 48+48+48 |
Vertices | 48 |
Vertex figure | Isosceles-trapezoidal scalene, edge lengths 1, 1, 1, √2 (base trapezoid), √3 (top), √2 (side edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Thiddip–hip–thiddip: |
Squappip–squap–squappip: 120° | |
Thiddip–hip–shiddip: = | |
Thiddip–trip–squappip: 90° | |
Shiddip–cube–squappip: 90° | |
Central density | 1 |
Number of external pieces | 16 |
Level of complexity | 40 |
Related polytopes | |
Army | Hasquap |
Regiment | Hasquap |
Dual | Hexagonal-square antitegmatic duotegum |
Conjugate | Hexagonal-square antiprismatic duoprism |
Abstract & topological properties | |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | G2×I2(8)×A1+, order 192 |
Convex | Yes |
Nature | Tame |
The hexagonal-square antiprismatic duoprism or hasquap is a convex uniform duoprism that consists of 6 square antiprismatic prisms, 2 square-hexagonal duoprisms, and 8 triangular-hexagonal duoprisms. Each vertex joins 2 square antiprismatic prisms, 3 triangular-hexagonal duoprisms, and 1 square-hexagonal duoprism.
Vertex coordinates[edit | edit source]
The vertices of a hexagonal-square antiprismatic duoprism of edge length 1 are given by:
Representations[edit | edit source]
A hexagonal-square antiprismatic duoprism has the following Coxeter diagrams:
- x6o s2s8o (full symmetry; square antiprisms as alternated octagonal prisms)
- x6o s2s4s (square antiprisms as alternated ditetragonal prisms)
- x3x s2s8o (hexagons as ditrigons)
- x3x s2s4s