Decachoric prism
Jump to navigation
Jump to search
Decachoric prism | |
---|---|
File:Decachoric prism.png | |
Rank | 5 |
Type | Uniform |
Notation | |
Bowers style acronym | Decap |
Coxeter diagram | x o3x3x3o () |
Elements | |
Tera | 10 truncated tetrahedral prisms, 2 decachora |
Cells | 20 triangular prisms, 20 hexagonal prisms, 20 truncated tetrahedra |
Faces | 40 triangles, 60 squares, 40 hexagons |
Edges | 30+120 |
Vertices | 60 |
Vertex figure | Tetragonal disphenoidal pyramid, edge lengths 1, √3 (base), √2 (legs) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Diteral angles | Tuttip–hip–tuttip: |
Deca–tut–tuttip: 90° | |
Tuttip–trip–tuttip: | |
Height | 1 |
Central density | 1 |
Number of external pieces | 12 |
Level of complexity | 15 |
Related polytopes | |
Army | Decap |
Regiment | Decap |
Dual | Bidecachoric tegum |
Conjugate | None |
Abstract & topological properties | |
Flag count | 7200 |
Euler characteristic | 2 |
Orientable | Yes |
Properties | |
Symmetry | A4×2×A1, order 480 |
Convex | Yes |
Nature | Tame |
The decachoric prism or decap is a prismatic uniform polyteron that consists of 2 decachora and 10 truncated tetrahedral prisms. 1 decachoron and 4 truncated tetrahedral prisms join at each vertex. As the name suggests, it can be obtained as a prism based on the decachoron, which also makes it a convex segmentoteron.
Vertex coordinates[edit | edit source]
The vertices of a decachoric prism of edge length 1 are given by:
External links[edit | edit source]
- Klitzing, Richard. "Decap".