6-demicube
| Demihexeract (6-demicube) | ||
|---|---|---|
Petrie polygon projection | ||
| Type | Uniform 6-polytope | |
| Family | demihypercube | |
| Schläfli symbol | {3,33,1} = h{4,34} s{21,1,1,1,1} | |
| Coxeter diagrams | = =
| |
| 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, [33,1,1] = [1+,4,34] [25]+ | |
| Petrie polygon | decagon | |
| Properties | convex | |
In geometry, a 6-demicube, demihexeract or hemihexeract is a uniform 6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes. Acronym: hax.
E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as HM6 for a 6-dimensional half measure polytope.
Coxeter named this polytope as 131 from its Coxeter diagram, with a ring on one of the 1-length branches, . It can named similarly by a 3-dimensional exponential Schläfli symbol or {3,33,1}.
