Demienneract (9-demicube) | ||
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![]() 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 |
Ingeometry, a demienneractor9-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] |
Fundamental convex regular and uniform polytopes in dimensions 2–10
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Family | An | Bn | I2(p) / Dn | E6 / E7 / E8 / F4 / G2 | Hn | |||||||
Regular polygon | Triangle | Square | p-gon | Hexagon | Pentagon | |||||||
Uniform polyhedron | Tetrahedron | Octahedron • Cube | Demicube | Dodecahedron • Icosahedron | ||||||||
Uniform polychoron | Pentachoron | 16-cell • Tesseract | Demitesseract | 24-cell | 120-cell • 600-cell | |||||||
Uniform 5-polytope | 5-simplex | 5-orthoplex • 5-cube | 5-demicube | |||||||||
Uniform 6-polytope | 6-simplex | 6-orthoplex • 6-cube | 6-demicube | 122 • 221 | ||||||||
Uniform 7-polytope | 7-simplex | 7-orthoplex • 7-cube | 7-demicube | 132 • 231 • 321 | ||||||||
Uniform 8-polytope | 8-simplex | 8-orthoplex • 8-cube | 8-demicube | 142 • 241 • 421 | ||||||||
Uniform 9-polytope | 9-simplex | 9-orthoplex • 9-cube | 9-demicube | |||||||||
Uniform 10-polytope | 10-simplex | 10-orthoplex • 10-cube | 10-demicube | |||||||||
Uniform n-polytope | n-simplex | n-orthoplex • n-cube | n-demicube | 1k2 • 2k1 • k21 | n-pentagonal polytope | |||||||
Topics: Polytope families • Regular polytope • List of regular polytopes and compounds |