5-demicube

In five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices truncated.

It was discovered by Thorold Gosset. Since it was the only semiregular 5-polytope (made of more than one type of regular facets), he called it a 5-ic semi-regular. E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as HM₅ for a 5-dimensional half measure polytope.

Coxeter named this polytope as 1₂₁ from its Coxeter diagram, which has branches of length 2, 1 and 1 with a ringed node on one of the short branches, and Schläfli symbol ${\displaystyle \left\{3{\begin{array}{l}3,3\\3\end{array}}\right\}}$ or {3,3^2,1}.

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