Triangular-tetrahedral duoprismatic prism
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Triangular-tetrahedral duoprismatic prism | |
---|---|
Rank | 6 |
Type | Uniform |
Notation | |
Bowers style acronym | Tratepe |
Coxeter diagram | x x3o x3o3o () |
Tapertopic notation | 12111 |
Elements | |
Peta | 2 triangular-tetrahedral duoprisms, 3 square-tetrahedral duoprisms, 4 triangular duoprismatic prisms |
Tera | 3+6 tetrahedral prisms, 8 triangular duoprisms, 6+12 triangular-square duoprisms |
Cells | 6 tetrahedra, 4+12+12+24 triangular prisms, 18 cubes |
Faces | 8+24 triangles, 12+18+36 squares |
Edges | 12+24+36 |
Vertices | 24 |
Vertex figure | Triangular scalenic pyramid, edge lengths 1 (base triangle and top edge of base) and √2 (remaining edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dipetal angles | Tratet–tepe–squatet: 90° |
Tratet–triddip–tratrip: 90° | |
Squatet–tisdip–tratrip: 90° | |
Tratrip–tisdip–tratrip: | |
Squatet–tepe–squatet: 60° | |
Heights | Tratet atop tratet: 1 |
Tepe atop squatet: | |
Trip atop tratrip: | |
Tisdip atop ortho tisdip: | |
Central density | 1 |
Number of external pieces | 9 |
Level of complexity | 60 |
Related polytopes | |
Army | Tratepe |
Regiment | Tratepe |
Dual | Triangular-tetrahedral duotegmatic tegum |
Conjugate | None |
Abstract & topological properties | |
Flag count | 17280 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | A3×A2×A1, order 288 |
Convex | Yes |
Nature | Tame |
The triangular-tetrahedral duoprismatic prism or tratepe is a convex uniform duoprism that consists of 2 triangular-tetrahedral duoprisms, 3 square-tetrahedral duoprisms, and 4 triangular duoprismatic prisms. Each vertex joins 1 triangular-tetrahedral duoprism, 2 square-tetrahedral duoprisms, and 3 triangular duoprismatic prisms. As the name suggests, it is a prism based on the triangular-tetrahedral duoprism, which also makes it a convex segmentopeton.
Vertex coordinates[edit | edit source]
The vertices of a triangular-tetrahedral duoprismatic prism of edge length 1 are given by all even sign changes of the last three coordinates of:
External links[edit | edit source]
- Klitzing, Richard. "tratepe".