Special cut

The special cuts are a set of 314,248,344 4-dimensional Blind polytopes formed by diminishing the hexicosichoron (600-cell), i.e. removing non-adjacent sets of vertices and taking the convex hull of the remaining vertices. Each diminishing removes 20 tetrahedra and replaces them with an icosahedron. Roughly speaking, they are the 4-dimensional analogue of the three Johnson solids formed by diminishing the icosahedron (diminished icosahedron, metabidiminished icosahedron, and tridiminished icosahedron). The special cuts have no generalization to higher dimensions.