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}.
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 | B9 | D9 | D8 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [18]+ = [9] | [16] | [14] |
Graph | |||
Coxeter plane | D7 | D6 | |
Dihedral symmetry | [12] | [10] | |
Coxeter group | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A7 | A5 | A3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
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}.
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 | B9 | D9 | D8 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [18]+ = [9] | [16] | [14] |
Graph | |||
Coxeter plane | D7 | D6 | |
Dihedral symmetry | [12] | [10] | |
Coxeter group | D5 | D4 | D3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |
Coxeter plane | A7 | A5 | A3 |
Graph | |||
Dihedral symmetry | [8] | [6] | [4] |