Puneet Varma (Editor)

8 demicube

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8-demicube

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.

Contents

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 { 3 3 , 3 , 3 , 3 , 3 3 } 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:

(±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:

References

8-demicube Wikipedia


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