Demienneract (9-demicube) | ||
---|---|---|
Petrie polygon | ||
Type | Uniform 9-polytope | |
Family | demihypercube | |
Coxeter symbol | 1_{61} | |
Schläfli symbol | {3,3^{6,1}} = h{4,3^{7}} s{2^{1,1,1,1,1,1,1,1}} | |
Coxeter-Dynkin diagram | = | |
8-faces | 274 | 18 {3^{1,5,1}} 256 {3^{7}} |
7-faces | 2448 | 144 {3^{1,4,1}} 2304 {3^{6}} |
6-faces | 9888 | 672 {3^{1,3,1}} 9216 {3^{5}} |
5-faces | 23520 | 2016 {3^{1,2,1}} 21504 {3^{4}} |
4-faces | 36288 | 4032 {3^{1,1,1}} 32256 {3^{3}} |
Cells | 37632 | 5376 {3^{1,0,1}} 32256 {3,3} |
Faces | 21504 | {3} |
Edges | 4608 | |
Vertices | 256 | |
Vertex figure | Rectified 8-simplex | |
Symmetry group | D_{9}, [3^{6,1,1}] = [1^{+},4,3^{7}] [2^{8}]^{+} | |
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 HM_{9} for a 9-dimensional half measure polytope.
Coxeter named this polytope as 1_{61} from its Coxeter diagram, with a ring on one of the 1-length branches, and Schläfli symbol or {3,3^{6,1}}.
Cartesian coordinates for the vertices of a demienneract centered at the origin are alternate halves of the enneract:
with an odd number of plus signs.
Coxeter plane | B_{9} | D_{9} | D_{8} |
---|---|---|---|
Graph | |||
Dihedral symmetry | [18]^{+} = [9] | [16] | [14] |
Graph | |||
Coxeter plane | D_{7} | D_{6} | |
Dihedral symmetry | [12] | [10] | |
Coxeter group | D_{5} | D_{4} | D_{3} |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A_{7} | A_{5} | A_{3} |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |