Blind polytope

The Blind polytopes are the strictly 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 precisely the convex semiregular polytopes. The non-uniform ones are:
 * the 92 Johnson solids (3-dimensional),
 * the simplicial bipyramids (generalizing the triangular bipyramid, one in each dimension greater than 3),
 * the orthoplecial pyramids (generalizing the square pyramid, one in each dimension greater than 3),
 * 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), minus the semiregular snub disicositetrachoron.

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, including the snub disicositetrachoron. The only asymmetrical Blind polytopes are found in the special cuts.