Blind polytope

The Blind polytopes are the convex polytopes whose facets are all regular. As such, they are a subclass of the convex regular-faced polytopes, and the non-uniform Blind polytopes generalize the Johnson solids. Blind polytopes are named after the researching German couple Gerd and Roswitha Blind, who listed all such polytopes in a series of papers during the 1980s.

The uniform Blind polytopes are known as the semiregular polytopes. The non-uniform ones are:
 * the Johnson solids (3-dimensional),
 * the simplicial bipyramids (generalizing the triangular bipyramid, one in each dimension),
 * the orthoplecial pyramids (generalizing the square pyramid, one in each dimension),
 * the icosahedral pyramid (4-dimensional),
 * the icosahedral bipyramid (4-dimensional),
 * the augmented rectified pentachoron (4-dimensional),
 * and the special cuts of the hexacosichoron (4-dimensional).

In 2008 Mathieu Dutour Sikirić and Wendy Myrvold finally managed to provide the number of polytopes in the last class to be 314,248,344.