 It can be named by an extended Schläfli symbol {3,3k,2}.The family starts uniquely as 6-polytopes, but can be extended backwards to include the 5-demicube (demipenteract) in 5-dimensions, and the 4-simplex (5-cell) in 4-dimensions.Each polytope is constructed from 1k-1,2 and (n-1)-demicube facets.