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7-demicube
Uniform 7-polytope / From Wikipedia, the free encyclopedia
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.
More information Demihepteract ...
Demihepteract (7-demicube) | ||
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![]() 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 |
Close
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}.