8-demicube

Demiocteract
(8-demicube)

Petrie polygon projection
Type Uniform 8-polytope
Family demihypercube
Coxeter symbol 151
Schläfli symbol {31,1,5}
h{4,3,3,3,3,3,3}
s{2,2,2,2,2,2,2}
Coxeter-Dynkin diagram

7-faces 144:
16 {31,4,1}
128 {36}
6-faces 112 {31,3,1}
1024 {35}
5-faces 448 {31,2,1}
3584 {34}
4-faces 1120 {31,1,1}
7168 {3,3,3}
Cells 10752:
1792 {31,0,1}
8960 {3,3}
Faces 7168 {3}
Edges 1792
Vertices 128
Vertex figure Rectified 7-simplex
Symmetry group D8, [37,1,1] = [1+,4,36]
[27]+
Dual ?
Properties convex

In geometry, a demiocteract or 8-demicube is a uniform 8-polytope, constructed from the 8-hypercube, octeract, with alternated vertices deleted. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes.

Coxeter named this polytope as 151 from its Coxeter-Dynkin diagram, with a ring on one of the 1-length branches.

Contents

Cartesian coordinates

Cartesian coordinates for the vertices of a 8-demicube centered at the origin are alternate halves of the 8-cube:

(±1,±1,±1,±1,±1,±1,±1,±1)

with an odd number of plus signs.

Related polytopes and honeycombs

This polytope is the vertex figure for the uniform tessellation, 251 with Coxeter-Dynkin diagram:

Images

orthographic projections
Coxeter plane B8 D8 D7 D6 D5
Graph
Dihedral symmetry [16/2] [14] [12] [10] [8]
Coxeter plane D4 D3 A7 A5 A3
Graph
Dihedral symmetry [6] [4] [8] [6] [4]

References

External links