8-demicube

Demiocteract (8-demicube)
Petrie polygon projection
Type	Uniform 8-polytope
Family	demihypercube
Coxeter symbol	151
Schläfli symbols	{3,35,1} = h{4,36} s{21,1,1,1,1,1,1}
Coxeter diagrams	=
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, [35,1,1] = [1+,4,36] A18, [27]+
Dual	?
Properties	convex

In

E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as HM₈ for an 8-dimensional half measure polytope.

${\displaystyle \left\{3{\begin{array}{l}3,3,3,3,3\\3\end{array}}\right\}}$

Cartesian coordinates

:

(±1,±1,±1,±1,±1,±1,±1,±1)

with an odd number of plus signs.

Related polytopes and honeycombs

This polytope is the

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

• H.S.M. Coxeter:
  • Coxeter,
    ISBN 0-486-61480-8
    , p. 296, Table I (iii): Regular Polytopes, three regular polytopes in n-dimensions (n≥5)
  • H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973, p. 296, Table I (iii): Regular Polytopes, three regular polytopes in n-dimensions (n≥5)
  • Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
    ISBN 978-0-471-01003-6 [1]
    • (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
    • (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
    • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
• ISBN 978-1-56881-220-5
  (Chapter 26. pp. 409: Hemicubes: 1_n1)