The family was named by their Coxeter symbol 1k2 by its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 1-node sequence.
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 has a vertex figure of a {31,n-2,2} polytope is a birectified n-simplex, t2{3n}.
The sequence ends with k=6 (n=10), as an infinite tessellation of 9-dimensional hyperbolic space.