Square-hexagonal duoprism
(Redirected from 4-6 duoprism)
Square-hexagonal duoprism | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Shiddip |
Coxeter diagram | x4o x6o () |
Elements | |
Cells | 6 cubes, 4 hexagonal prisms |
Faces | 6+24 squares, 4 hexagons |
Edges | 24+24 |
Vertices | 24 |
Vertex figure | Digonal disphenoid, edge lengths √3 (base 1) and √2 (base 2 and sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Cube–4–cube: 120° |
Cube–4–hip: 90° | |
Hip–4–hip: 90° | |
Height | 1 |
Central density | 1 |
Number of external pieces | 10 |
Level of complexity | 6 |
Related polytopes | |
Army | Shiddip |
Regiment | Shiddip |
Dual | Square-hexagonal duotegum |
Conjugate | None |
Abstract & topological properties | |
Flag count | 576 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | B2×G2, order 96 |
Flag orbits | 6 |
Convex | Yes |
Nature | Tame |
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.
Gallery[edit | edit source]
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×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)
External links[edit | edit source]
- Bowers, Jonathan. "Category A: duoprisms".
- Klitzing, Richard. "shiddip".
- Wikipedia contributors. "4-6 duoprism".