Petrie polygon projection
TypeUniform 8-polytope
Coxeter symbol 151
Schläfli symbols{3,35,1} = h{4,36}
Coxeter diagrams =

16 {31,4,1}
128 {36}
6-faces112 {31,3,1}
1024 {35}
5-faces448 {31,2,1}
3584 {34}
4-faces1120 {31,1,1}
7168 {3,3,3}
1792 {31,0,1}
8960 {3,3}
Faces7168 {3}
Vertex figureRectified 7-simplex
Symmetry groupD8, [37,1,1] = [1+,4,36]
A18, [27]+

In geometry, a demiocteract or 8-demicube is a uniform 8-polytope, constructed from the 8-hypercube, octeract, with alternated vertices truncated. 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 HM8 for an 8-dimensional half measure polytope.

Coxeter named this polytope as 151 from its Coxeter diagram, with a ring on one of the 1-length branches, and Schläfli symbol or {3,35,1}.

Cartesian coordinates

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


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:


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


External links

Fundamental convex regular and uniform polytopes in dimensions 2–10
Family An Bn I2(p) / Dn E6 / E7 / E8 / E9 / E10 / F4 / G2 Hn
Regular polygon Triangle Square p-gon Hexagon Pentagon
Uniform polyhedron Tetrahedron OctahedronCube Demicube DodecahedronIcosahedron
Uniform 4-polytope 5-cell 16-cellTesseract Demitesseract 24-cell 120-cell600-cell
Uniform 5-polytope 5-simplex 5-orthoplex5-cube 5-demicube
Uniform 6-polytope 6-simplex 6-orthoplex6-cube 6-demicube 122221
Uniform 7-polytope 7-simplex 7-orthoplex7-cube 7-demicube 132231321
Uniform 8-polytope 8-simplex 8-orthoplex8-cube 8-demicube 142241421
Uniform 9-polytope 9-simplex 9-orthoplex9-cube 9-demicube
Uniform 10-polytope 10-simplex 10-orthoplex10-cube 10-demicube
Uniform n-polytope n-simplex n-orthoplexn-cube n-demicube 1k22k1k21 n-pentagonal polytope
Topics: Polytope familiesRegular polytopeList of regular polytopes and compounds
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