| Demihexeract (6-demicube) |
||
|---|---|---|
Petrie polygon projection |
||
| Type | Uniform 6-polytope | |
| Family | demihypercube | |
| Schläfli symbol | {3,33,1} h{4,3,3,3,3} s{2,2,2,2,2} |
|
| Coxeter-Dynkin diagram | ||
| Coxeter symbol | 131 | |
| 5-faces | 44 | 12 {31,2,1} 32 {34} |
| 4-faces | 252 | 60 {31,1,1} 192 {33} |
| Cells | 640 | 160 {31,0,1} 480 {3,3} |
| Faces | 640 | {3} |
| Edges | 240 | |
| Vertices | 32 | |
| Vertex figure | Rectified 5-simplex |
|
| Symmetry group | D6, [35,1,1] = [1+,4,34] [25]+ |
|
| Petrie polygon | decagon | |
| Properties | convex | |
In geometry, a 6-demicube or demihexteract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternate vertices deleted. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes.
Coxeter named this polytope as 131 from its Coxeter-Dynkin diagram, with a ring on one of the 1-length Coxeter-Dynkin diagram branches. It can named similarly by a 3-dimensional exponential Schläfli symbol, {3,33,1}.
Contents |
Cartesian coordinates for the vertices of a demihexeract centered at the origin are alternate halves of the hexeract:
with an odd number of plus signs.
| Coxeter plane | B6 | |
|---|---|---|
| Graph | ||
| Dihedral symmetry | [12/2] | |
| Coxeter plane | D6 | D5 |
| Graph | ||
| Dihedral symmetry | [10] | [8] |
| Coxeter plane | D4 | D3 |
| Graph | ||
| Dihedral symmetry | [6] | [4] |
| Coxeter plane | A5 | A3 |
| Graph | ||
| Dihedral symmetry | [6] | [4] |
There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique:
t0(131) |
t0,1(131) |
t0,2(131) |
t0,3(131) |
t0,4(131) |
t0,1,2(131) |
t0,1,3(131) |
t0,1,4(131) |
t0,2,3(131) |
t0,2,4(131) |
t0,3,4(131) |
t0,1,2,3(131) |
t0,1,2,4(131) |
t0,1,3,4(131) |
t0,2,3,4(131) |
t0,1,2,3,4(131) |