Square-hexagonal duoprism

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Square-hexagonal duoprism
4-6 duoprism.png
Rank4
TypeUniform
SpaceSpherical
Bowers style acronymShiddip
Coxeter diagramx4o x6o (CDel node 1.pngCDel 4.pngCDel node.pngCDel 2.pngCDel node 1.pngCDel 6.pngCDel node.png)
Elements
Cells6 cubes, 4 hexagonal prisms
Faces6+24 squares, 4 hexagons
Edges24+24
Vertices24
Vertex figureDigonal disphenoid, edge lengths 3 (base 1) and 2 (base 2 and sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesCube–4–cube: 120°
 Cube–4–hip: 90°
 Hip–4–hip: 90°
Height1
Central density1
Number of pieces10
Level of complexity6
Related polytopes
ArmyShiddip
RegimentShiddip
DualSquare-hexagonal duotegum
ConjugateNone
Abstract properties
Euler characteristic0
Topological properties
OrientableYes
Properties
SymmetryB2×G2, order 96
ConvexYes
NatureTame

The square-hexagonal duoprism or shiddip, also known as the 4-6 duoprism, is a uniform duoprism that consists of 4 hexagonal prisms and 6 cubes, with two of each joining at each vertex.s.

It is also a CRF segmentochoron, being hexagonal prism atop hexagonal prism. It is designated K-4.54 on Richard Klitzing's list. As It can thus be thought of as a prism based on the hexagonal prism.

This polychoron can be alternated into a digonal-triangular duoantiprism, although it cannot be made uniform.

Vertex coordinates[edit | edit source]

The vertices of a square-hexagonal duoprism of edge length 1, centered at the origin, are given by:

Representations[edit | edit source]

A square-hexagonal duoprism has the following Coxeter diagrams:

  • x4o x6o (full symmetry)
  • x x x6o (G2×A2×A2 symmetry, square as rectangle)
  • x3x x4o (A2×BC2 symmetry, hexagon as ditrigon)
  • x x x3x (A2×A1×A1 symmetry, both above combined
  • xx xx6oo&#x (G2×A1 axial, hexagonal prism prism)
  • xx xx3xx&#x (A2×A1 symmetry, as above with ditrigon symmetry)
  • xux xxx4ooo&#xt (BC2×A1 axial, cube-first)
  • xux xxx xxx&#xt (A1×A1×A1 axial, cube-first)
  • oqo xxx6ooo&#xt (G2×A1 axial, hexagon-first)
  • oqo xxx3xxx&#xt (A2×A1 axial, hexagon-first)

External links[edit | edit source]