8-demicube

In geometry, a demiocteract or 8-demicube is a uniform 8-polytope, constructed from the 8-hypercube, octeract, 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 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 $$\left\{3 \begin{array}{l}3, 3, 3, 3, 3\\3\end{array}\right\}$$ 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: