Bitruncated 6-simplex
(Redirected from Bitruncated heptapeton)
Bitruncated 6-simplex | |
---|---|
Rank | 6 |
Type | Uniform |
Notation | |
Bowers style acronym | Batal |
Coxeter diagram | o3x3x3o3o3o () |
Elements | |
Peta | 7 truncated hexatera, 7 bitruncated hexatera |
Tera | 21 pentachora, 42 truncated pentachora, 21 decachora |
Cells | 105 tetrahedra, 35+105 truncated tetrahedra |
Faces | 35+210 triangles, 140 hexagons |
Edges | 105+210 |
Vertices | 105 |
Vertex figure | Tetrahedral scalene , edge lengths 1 (base tetrahedron and top edge) and √3 (sides) |
Measures (edge length 1) | |
Circumradius | |
Hypervolume | |
Dipetal angles | Tix-tip-bittix: |
Bittix-deca-bittix: | |
Tix-pen-tix: | |
Central density | 1 |
Number of external pieces | 14 |
Level of complexity | 15 |
Related polytopes | |
Army | Batal |
Regiment | Batal |
Conjugate | None |
Abstract & topological properties | |
Flag count | 75600 |
Euler characteristic | 0 |
Orientable | Yes |
Properties | |
Symmetry | A6, order 5040 |
Convex | Yes |
Nature | Tame |
The bitruncated 6-simplex (also called the bitruncated heptapeton or batal) is a convex uniform 6-polytope. It consists of 7 truncated hexatera and 7 bitruncated hexatera as facets. 2 truncated hexatera and 4 bitruncated hexatera join at each vertex. As the name suggests, it is the bitruncation of the 6-simplex.
Vertex coordinates[edit | edit source]
The vertices of a bitruncated 6-simplex of edge length 1 can be given in seven dimensions as all permutations of:
- .
Representations[edit | edit source]
A bitruncated 6-simplex has the following Coxeter diagrams:
- o3x3x3o3o3o () (full symmetry)
- xoo3xux3oox3ooo3ooo&#xt (A5 axial, truncated hexateron-first)
Gallery[edit | edit source]
-
A5 orthographic projection
-
A4
-
A3
-
A2
External links[edit | edit source]
- Klitzing, Richard. "batal".
- Wikipedia contributors. "Bitruncated 6-simplex".