Hexagonal-dodecagrammic duoprism
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Hexagonal-dodecagrammic duoprism | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Coxeter diagram | x6o x12/5o () |
Elements | |
Cells | 12 hexagonal prisms, 6 dodecagrammic prisms |
Faces | 72 squares, 12 hexagons, 6 dodecagrams |
Edges | 72+72 |
Vertices | 72 |
Vertex figure | Digonal disphenoid, edge lengths √3 (base 1), (√6–√2)/2 (base 2), √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Stwip–12/5–stwip: 120° |
Hip–4–stwip: 90° | |
Hip–6–hip: 30° | |
Central density | 5 |
Number of external pieces | 30 |
Level of complexity | 12 |
Related polytopes | |
Army | Semi-uniform hitwadip |
Dual | Hexagonal-dodecagrammic duotegum |
Conjugate | Hexagonal-dodecagonal duoprism |
Abstract & topological properties | |
Flag count | 1728 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | G2×I2(12), order 288 |
Convex | No |
Nature | Tame |
The hexagonal-dodecagrammic duoprism, also known as the 6-12/5 duoprism, is a uniform duoprism that consists of 12 hexagonal prisms and 6 dodecagrammic prisms, with 2 of each at each vertex.
Vertex coordinates[edit | edit source]
The coordinates of a hexagonal-dodecagrammic duoprism, centered at the origin and with unit edge length, are given by:
- ,
- ,
- ,
- ,
- ,
- .
Representations[edit | edit source]
A hexagonal-dodecagrammic duoprism has the following Coxeter diagrams:
- x6o x12/5o () (full symmetry)
- x3x x12/5o () (A2×I2(12) symmetry, hexagons as ditrigons)
- x6o x6/5x () (G2×G2 symmetry, dodecagrams as dihexagrams)
- x3x x6/5x () (A2×G2 symmetry)
External links[edit | edit source]
- Bowers, Jonathan. "Category A: Duoprisms".
- Klitzing, Richard. "nd-mb-dip".