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## Summary

Demienneract
(9-demicube) Petrie polygon
Type Uniform 9-polytope
Family demihypercube
Coxeter symbol 161
Schläfli symbol {3,36,1} = h{4,37}
s{21,1,1,1,1,1,1,1}
Coxeter-Dynkin diagram               =                                  8-faces 274 18 {31,5,1} 256 {37} 7-faces 2448 144 {31,4,1} 2304 {36} 6-faces 9888 672 {31,3,1} 9216 {35} 5-faces 23520 2016 {31,2,1} 21504 {34} 4-faces 36288 4032 {31,1,1} 32256 {33} Cells 37632 5376 {31,0,1} 32256 {3,3} Faces 21504 {3} Edges 4608
Vertices 256
Vertex figure Rectified 8-simplex Symmetry group D9, [36,1,1] = [1+,4,37]
+
Dual ?
Properties convex

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.

## Images

orthographic projections
Coxeter plane B9 D9 D8
Graph
Dihedral symmetry + =   
Graph
Coxeter plane D7 D6
Dihedral symmetry  
Coxeter group D5 D4 D3
Graph
Dihedral symmetry   
Coxeter plane A7 A5 A3
Graph
Dihedral symmetry