10-demicube

Demidekeract
(10-demicube) Petrie polygon projection
Type Uniform 10-polytope
Family demihypercube
Coxeter symbol 171
Schläfli symbol {31,7,1}
h{4,38}
s{21,1,1,1,1,1,1,1,1}
Coxeter diagram                 =                                      9-faces 532 20 {31,6,1} 512 {38} 8-faces 5300 180 {31,5,1} 5120 {37} 7-faces 24000 960 {31,4,1} 23040 {36} 6-faces 64800 3360 {31,3,1} 61440 {35} 5-faces 115584 8064 {31,2,1} 107520 {34} 4-faces 142464 13440 {31,1,1} 129024 {33} Cells 122880 15360 {31,0,1} 107520 {3,3} Faces 61440 {3} Edges 11520
Vertices 512
Vertex figure Rectified 9-simplex Symmetry group D10, [37,1,1] = [1+,4,38]
+
Dual ?
Properties convex

In geometry, a 10-demicube or demidekeract is a uniform 10-polytope, constructed from the 10-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 HM10 for a ten-dimensional half measure polytope.

Coxeter named this polytope as 171 from its Coxeter diagram, with a ring on one of the 1-length branches,                 and Schläfli symbol $\left\{3{\begin{array}{l}3,3,3,3,3,3,3\\3\end{array}}\right\}$ or {3,37,1}.

Cartesian coordinates

Cartesian coordinates for the vertices of a demidekeract centered at the origin are alternate halves of the dekeract:

(±1,±1,±1,±1,±1,±1,±1,±1,±1,±1)

with an odd number of plus signs.

Images B10 coxeter plane D10 coxeter plane(Vertices are colored by multiplicity: red, orange, yellow, green = 1,2,4,8)