# Square-hexagonal duoprism

Square-hexagonal duoprism Rank4
TypeUniform
SpaceSpherical
Bowers style acronymShiddip
Coxeter diagramx4o x6o (       )
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$\frac{\sqrt6}{2} ≈ 1.22475$ Hypervolume$\frac{3\sqrt3}{2} ≈ 2.59808$ 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

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

• $\left(±\frac12,\,±\frac12,\,0,\,±1\right),$ • $\left(±\frac12,\,±\frac12,\,±\frac{\sqrt3}{2},\,±\frac12\right).$ ## Representations

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)