Triangular-cubic duoprism
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Triangular-cubic duoprism | |
---|---|
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Tracube |
Coxeter diagram | x3o x4o3o () |
Tapertopic notation | 11111 |
Elements | |
Tera | 6 triangular-square duoprisms, 3 tesseracts |
Cells | 12 triangular prisms, 3+18 cubes |
Faces | 8 triangles, 18+36 squares |
Edges | 24+36 |
Vertices | 24 |
Vertex figure | Triangular scalene, edge lengths 1 (top), √2 (base triangle and sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Tes–cube–tisdip: 90° |
Tisdip–trip–tisdip: 90° | |
Tes–cube–tes: 60° | |
Heights | Tisdip atop tisdip: 1 |
Cube atop tes: | |
Central density | 1 |
Number of external pieces | 9 |
Level of complexity | 10 |
Related polytopes | |
Army | Tracube |
Regiment | Tracube |
Dual | Triangular-octahedral duotegum |
Conjugate | None |
Abstract & topological properties | |
Flag count | 2880 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | B3×A2, order 288 |
Convex | Yes |
Nature | Tame |
The triangular-cubic duoprism or tracube, also known as a triangular-square duoprismatic prism, is a convex uniform duoprism that consists of 3 tesseracts and 6 triangular-square duoprisms. Each vertex joins 2 tesseracts and 3 triangular-square duoprisms. It is a duoprism based on a triangle and a cube, which makes it a convex segmentoteron, and it can also be viewed as a duoprism based on a square and a triangular prism.
Vertex coordinates[edit | edit source]
The vertices of a triangular-cubic duoprism of edge length 1 are given by:
Representations[edit | edit source]
A triangular-cubic duoprism has the following Coxeter diagrams:
- x3o x4o3o (full symmetry)
- x x3o x4o (triangular-square duoprismatic prism)
- x x x x3o (triangular prismatic prismatic prism)
- xx3oo xx4oo&#x (triangular-square duoprism atop triangular-square duoprism)
- xx3oo xx xx&#x
- ox xx xx4oo&#x (cube atop tesseract)
- ox xx xx xx&#x
- xxx xxx xxx&#x
External links[edit | edit source]
- Klitzing, Richard. "tracube".
- Hi.gher.Space Wiki Contributors. "Triangular triprism".