Hexagonal-square antiprismatic duoprism

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Hexagonal-square antiprismatic duoprism
Rank5
TypeUniform
Notation
Bowers style acronymHasquap
Coxeter diagramx6o s2s8o
Elements
Tera6 square antiprismatic prisms, 8 triangular-hexagonal duoprisms, 2 square-hexagonal duoprisms
Cells48 triangular prisms, 12 cubes, 6 square antiprisms, 8+8 hexagonal prisms
Faces48 triangles, 12+48+48 squares, 8 hexagons
Edges48+48+48
Vertices48
Vertex figureIsosceles-trapezoidal scalene, edge lengths 1, 1, 1, 2 (base trapezoid), 3 (top), 2 (side edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesThiddip–hip–thiddip:
 Squappip–squap–squappip: 120°
 Thiddip–hip–shiddip: =
 Thiddip–trip–squappip: 90°
 Shiddip–cube–squappip: 90°
 
Central density1
Number of external pieces16
Level of complexity40
Related polytopes
ArmyHasquap
RegimentHasquap
DualHexagonal-square antitegmatic duotegum
ConjugateHexagonal-square antiprismatic duoprism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryG2×I2(8)×A1+, order 192
ConvexYes
NatureTame

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