Triangular-pentachoric duoprismatic prism
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Triangular-pentachoric duoprismatic prism | |
---|---|
Rank | 7 |
Type | Uniform |
Notation | |
Bowers style acronym | Trippen |
Coxeter diagram | x x3o x3o3o3o () |
Tapertopic notation | 13111 |
Elements | |
Exa | 2 triangular-pentachoric duoprisms, 3 square-pentachoric duoprisms, 5 triangular-tetrahedral duoprismatic prisms |
Peta | 3+6 pentachoric prisms, 10 triangular-tetrahedral duoprisms, 15 square-tetrahedral duoprisms, 10 triangular duoprismatic prisms |
Tera | 6 pentachora, 15+30 tetrahedral prisms, 20 triangular duoprisms, 10+30 triangular-square duoprisms |
Cells | 30 tetrahedra, 5+20+30+60 triangular prisms, 30 cubes |
Faces | 10+60 triangles, 15+30+60 squares |
Edges | 15+30+60 |
Vertices | 30 |
Vertex figure | Tetrahedral scalenic pyramid, edge lengths 1 (base tetrahedron and top edge of base) and √2 (remaining edges) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diexal angles | Trapen–penp–squapen: 90° |
Trapen–tratet–tratepe: 90° | |
Squapen–squatet–tratepe: 90° | |
Tratepe–tratrip–tratepe: | |
Squapen–penp–squapen: 60° | |
Heights | Trapen atop trapen: 1 |
Penp atop squapen: | |
Trip atop tratepe: | |
Central density | 1 |
Number of external pieces | 10 |
Level of complexity | 105 |
Related polytopes | |
Army | Trippen |
Regiment | Trippen |
Dual | Triangular-pentachoric duotegmatic tegum |
Conjugate | None |
Abstract & topological properties | |
Flag count | 151200 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | A4×A2×A1, order 1440 |
Convex | Yes |
Nature | Tame |
The triangular-pentachoric duoprismatic prism or trippen is a convex uniform duoprism that consists of 2 triangular-pentachoric duoprisms, 3 square-pentachoric duoprisms, and 5 triangular-tetrahedral duoprismatic prisms. Each vertex joins 1 triangular-pentachoric duoprism, 2 square-pentachoric duoprisms, and 4 triangular-tetrahedral duoprismatic prisms. As the name suggests, it is a prism based on the triangular-pentachoric duoprism, which also makes it a convex segmentoexon.
External links[edit | edit source]
- Klitzing, Richard. "trippen".