9-demicube

In geometry, a demienneract or 9-demicube is a uniform 9-polytope, constructed from the 9-cube, 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 HM9 for a 9-dimensional half measure polytope.

Coxeter named this polytope as 161 from its Coxeter diagram, with a ring on one of the 1-length branches, and Schläfli symbol $$\left\{3 \begin{array}{l}3, 3, 3, 3, 3, 3\\3\end{array}\right\}$$ or {3,36,1}.

Cartesian coordinates
Cartesian coordinates for the vertices of a demienneract centered at the origin are alternate halves of the enneract:
 * (±1,±1,±1,±1,±1,±1,±1,±1,±1)

with an odd number of plus signs.