9-demicube
| Demienneract (9-demicube) | ||
|---|---|---|
Petrie polygon | ||
| Type | Uniform 9-polytope | |
| Family | demihypercube | |
| Coxeter symbol | 161 | |
| Schläfli symbol | {3,36,1} = h{4,37} s{21,1,1,1,1,1,1,1} | |
| Coxeter-Dynkin diagram | = | |
| 8-faces | 274 | 18 {31,5,1} 256 {37} |
| 7-faces | 2448 | 144 {31,4,1} 2304 {36} |
| 6-faces | 9888 | 672 {31,3,1} 9216 {35} |
| 5-faces | 23520 | 2016 {31,2,1} 21504 {34} |
| 4-faces | 36288 | 4032 {31,1,1} 32256 {33} |
| Cells | 37632 | 5376 {31,0,1} 32256 {3,3} |
| Faces | 21504 | {3} |
| Edges | 4608 | |
| Vertices | 256 | |
| Vertex figure | Rectified 8-simplex | |
| Symmetry group | D9, [36,1,1] = [1+,4,37] [28]+ | |
| Dual | ? | |
| Properties | convex | |
In geometry, a demienneract or 9-demicube is a uniform 9-polytope, constructed from the 9-cube, with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes.
E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as HM9 for a 9-dimensional half measure polytope.
Coxeter named this polytope as 161 from its Coxeter diagram, with a ring on one of the 1-length branches, and Schläfli symbol or {3,36,1}.
