Blind polytope

In geometry, a Blind polytope is a convex polytope composed of regular polytope facets.
The category was named after the German couple Gerd and Roswitha Blind, who described them in a series of papers beginning in 1979.
It generalizes the set of semiregular polyhedra and Johnson solids to higher dimensions.

Uniform cases

The set of convex [uniform 4-polytope]s are completely known cases, nearly all grouped by their Wythoff constructions, sharing symmetries of the convex regular 4-polytopes and prismatic forms.
Set of convex uniform 5-polytopes, uniform 6-polytopes, uniform 7-polytopes, etc are largely enumerated as Wythoff constructions, but not known to be complete.

Other cases

Pyramidal forms:

Octahedral pyramid, ∨, an octahedron base, and 8 tetrahedra sides meeting at an apex.
Icosahedral pyramid, ∨, an icosahedron base, and 20 tetrahedra sides.

Bipyramid forms:

Tetrahedral bipyramid, +, a tetrahedron center, and 8 tetrahedral cells on two side.
Icosahedral bipyramid, +, an icosahedron center, and 40 tetrahedral cells on two sides.

Augmented forms:

Rectified 5-cell augmented with one octahedral pyramid, adding one vertex for 11 total. It retains 5 tetrahedral cells, reduced to 4 octahedral cells and adds 8 new tetrahedral cells.

Convex regular-faced polytopes

Blind polytopes are a subset of convex regular-faced polytopes.
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.