7-demicube
In geometry, a demihepteract or 7-demicube is a uniform 7-polytope, constructed from the 7-hypercube (hepteract) with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes.
| Demihepteract (7-demicube) | ||
|---|---|---|
Petrie polygon projection | ||
| Type | Uniform 7-polytope | |
| Family | demihypercube | |
| Coxeter symbol | 141 | |
| Schläfli symbol | {3,34,1} = h{4,35} s{21,1,1,1,1,1} | |
| Coxeter diagrams | =
| |
| 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, [34,1,1] = [1+,4,35] [26]+ | |
| Dual | ? | |
| Properties | convex | |
E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as HM7 for a 7-dimensional half measure polytope.
Coxeter named this polytope as 141 from its Coxeter diagram, with a ring on one of the 1-length branches, and Schläfli symbol or {3,34,1}.
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