The category was named after the German couple Gerd and Roswitha Blind, who described them in a series of papers beginning in 1979.
[1] It generalizes the set of semiregular polyhedra and Johnson solids to higher dimensions.
[2] The set of convex uniform 4-polytopes (also called semiregular 4-polytopes) are completely known cases, nearly all grouped by their Wythoff constructions, sharing symmetries of the convex regular 4-polytopes and prismatic forms.
[4] This much larger set allows CRF 4-polytopes to have Johnson solids as cells, as well as regular and semiregular polyhedral cells.
For example, a cubic bipyramid has 12 square pyramid cells.