Triangular duoprismatic prism
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Triangular duoprismatic prism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Tratrip |
Coxeter diagram | x x3o x3o () |
Tapertopic notation | 11111 |
Elements | |
Tera | 2 triangular duoprisms, 6 triangular-square duoprisms |
Cells | 6+12 triangular prisms, 9 cubes |
Faces | 12 triangles, 18+18 squares |
Edges | 9+36 |
Vertices | 18 |
Vertex figure | Tetragonal disphenoidal pyramid, edge lengths 1 (disphenoid bases) and √2 (remaining edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Triddip–trip–tisdip: 90º |
Tisdip–cube–tisdip: 90º | |
Tisdip–trip–tisdip: 60º | |
Heights | Triddip atop triddip: 1 |
Trip atop tisdip: √3/2 \approx 0.86603 | |
Central density | 1 |
Number of external pieces | 8 |
Level of complexity | 15 |
Related polytopes | |
Army | Tratrip |
Regiment | Tratrip |
Dual | Triangular duotegmatic tegum |
Conjugate | Triangular duoprismatic prism |
Abstract & topological properties | |
Flag count | 2160 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | A2≀S2×A1, order 144 |
Convex | Yes |
Nature | Tame |
The triangular duoprismatic prism or tratrip, also known as the triangular-triangular prismatic duoprism, is a convex uniform duoprism that consists of 2 triangular duoprisms and 6 triangular-square duoprisms. Each vertex joins 1 triangular duoprism and 4 triangular-square duoprisms. As the name suggests, it is a prism based on the triangular duoprism, which also makes it a convex segmentoteron.
Vertex coordinates[edit | edit source]
The vertices of a triangular duoprismatic prism of edge length 1 are given by:
Representations[edit | edit source]
A triangular duoprismatic prism has the following Coxeter diagrams:
- x x3o x3o (full symmetry)
- xx3oo xx3oo&#x (A2×A2 symmetry)
- ox xx xx3oo&#x (A2×A1×A1 symmetry, triangular prism atop triangular-square duoprism)
- xxx xxx3ooo&#x (A2×A1 symmetry, three different triangular prisms)
External links[edit | edit source]
- Klitzing, Richard. "tratrip".