| Demihepteract (7-demicube) |
||
|---|---|---|
Petrie polygon projection |
||
| Type | Uniform 7-polytope | |
| Family | demihypercube | |
| Coxeter symbol | 141 | |
| Schläfli symbol | {31,4,1} h{4,35} s{26} |
|
| Coxeter-Dynkin diagram | ||
| 6-faces | 78 | 14 {31,3,1} 64 {35} |
| 5-faces | 532 | 84 {31,2,1} 448 {34} |
| 4-faces | 1624 | 280 {31,1,1} 1344 {33} |
| Cells | 2800 | 560 {31,0,1} 2240 {3,3} |
| Faces | 2240 | {3} |
| Edges | 672 | |
| Vertices | 64 | |
| Vertex figure | Rectified 6-simplex |
|
| Symmetry group | D7, [36,1,1] = [1+,4,35] [26]+ |
|
| Dual | ? | |
| Properties | convex | |
In geometry, a demihepteract or 7-demicube is a uniform 7-polytope, constructed from the 7-hypercube (hepteract) with alternated vertices deleted. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes.
Coxeter named this polytope as 141 from its Coxeter-Dynkin diagram, with a ring on one of the 1-length Coxeter-Dynkin diagram branches.
Contents |
Cartesian coordinates for the vertices of a demihepteract centered at the origin are alternate halves of the hepteract:
with an odd number of plus signs.
| Coxeter plane | B7 | D7 | D6 |
|---|---|---|---|
| Graph | |||
| Dihedral symmetry | [14/2] | [12] | [10] |
| Coxeter plane | D5 | D4 | D3 |
| Graph | |||
| Dihedral symmetry | [8] | [6] | [4] |
| Coxeter plane | A5 | A3 | |
| Graph | |||
| Dihedral symmetry | [6] | [4] |
There are 95 uniform polytopes with D6 symmetry, 63 are shared by the B6 symmetry, and 32 are unique:
t0(141) |
t0,1(141) |
t0,2(141) |
t0,3(141) |
t0,4(141) |
t0,5(141) |
t0,1,2(141) |
t0,1,3(141) |
t0,1,4(141) |
t0,1,5(141) |
t0,2,3(141) |
t0,2,4(141) |
t0,2,5(141) |
t0,3,4(141) |
t0,3,5(141) |
t0,4,5(141) |
t0,1,2,3(141) |
t0,1,2,4(141) |
t0,1,2,5(141) |
t0,1,3,4(141) |
t0,1,3,5(141) |
t0,1,4,5(141) |
t0,2,3,4(141) |
t0,2,3,5(141) |
t0,2,4,5(141) |
t0,3,4,5(141) |
t0,1,2,3,4(141) |
t0,1,2,3,5(141) |
t0,1,2,4,5(141) |
t0,1,3,4,5(141) |
t0,2,3,4,5(141) |
t0,1,2,3,4,5(141) |