# Square-hexagonal duoprism

(Redirected from Square-ditrigonal duoprism)
Square-hexagonal duoprism
Rank4
TypeUniform
Notation
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${\displaystyle {\frac {\sqrt {6}}{2}}\approx 1.22475}$
Hypervolume${\displaystyle {\frac {3{\sqrt {3}}}{2}}\approx 2.59808}$
Dichoral anglesCube–4–cube: 120°
Cube–4–hip: 90°
Hip–4–hip: 90°
Height1
Central density1
Number of external pieces10
Level of complexity6
Related polytopes
ArmyShiddip
RegimentShiddip
DualSquare-hexagonal duotegum
ConjugateNone
Abstract & topological properties
Flag count576
Euler characteristic0
OrientableYes
Properties
SymmetryB2×G2, order 96
Flag orbits6
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:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,0,\,\pm 1\right)}$,
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {\sqrt {3}}{2}},\,\pm {\frac {1}{2}}\right)}$.

## Representations

A square-hexagonal duoprism has the following Coxeter diagrams:

• x4o x6o () (full symmetry)
• x x x6o () (G2×K2 symmetry, square as rectangle)
• x3x x4o () (A2×B2 symmetry, hexagon as ditrigon)
• x x x3x () (A2×K2 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 (B2×A1 axial, cube-first)
• xux xxx xxx&#xt (K3 axial, cube-first)
• oqo xxx6ooo&#xt (G2×A1 axial, hexagon-first)
• oqo xxx3xxx&#xt (A2×A1 axial, hexagon-first)