10 demicube

In geometry, a 10-demicube or demidekeract is a uniform 10-polytope, constructed from the 10-cube with alternated vertices truncated. 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 { 3 3 , 3 , 3 , 3 , 3 , 3 , 3 3 } or {3,3^7,1}.