10-demicube

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 or {3,37,1}. 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.