Triangular-dodecagonal duoprism
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Triangular-dodecagonal duoprism | |
---|---|
Rank | 4 |
Type | Uniform |
Notation | |
Bowers style acronym | Titwadip |
Coxeter diagram | x3o x12o () |
Elements | |
Cells | 12 triangular prisms, 3 dodecagonal prisms |
Faces | 12 triangles, 36 squares, 3 dodecagons |
Edges | 36+36 |
Vertices | 36 |
Vertex figure | Digonal disphenoid, edge lengths 1 (base 1), (√2+√6)/2 (base 2), and √2 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dichoral angles | Trip–3–trip: 150° |
Trip–4–twip: 90° | |
Twip–12–twip: 60° | |
Height | |
Central density | 1 |
Number of external pieces | 15 |
Level of complexity | 6 |
Related polytopes | |
Army | Titwadip |
Regiment | Titwadip |
Dual | Triangular-dodecagonal duotegum |
Conjugate | Triangular-dodecagrammic duoprism |
Abstract & topological properties | |
Flag count | 864 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | A2×I2(12), order 144 |
Flag orbits | 6 |
Convex | Yes |
Nature | Tame |
The triangular-dodecagonal duoprism or titwadip, also known as the 3-12 duoprism, is a uniform duoprism that consists of 3 dodecagonal prisms and 12 triangular prisms, with two of each joining at each vertex. It can also be seen as a convex segmentochoron, being a dodecagon atop a dodecagonal prism.
This polychoron can be subsymmetrically faceted into a 12-4 step prism, although it cannot be made uniform.
Vertex coordinates[edit | edit source]
The vertices of a triangular-dodecagonal duoprism of edge length 1, centered at the origin, are given by:
- ,
- ,
- ,
- ,
- ,
- .
Representations[edit | edit source]
A triangular-dodecagonal duoprism has the following Coxeter diagrams:
- x3o x12o () (full symetry)
- x3o x6x () (A2×G2 symmetry, dodecagon as dihexagon)
- ox xx12oo&#x (I2(12)×A1 axial, dodecagon atop dodecagon prism)
- ox xx6xx&#x (G2×A1 axial)
External links[edit | edit source]
- Bowers, Jonathan. "Category A: Duoprisms".
- Klitzing, Richard. "titwadip".