High Quality Content by WIKIPEDIA articles! In four dimensional geometry, Schlafli-Hess polychora are the complete set of 10 regular self-intersecting star polychora (four-dimensional polytopes). They are named in honor of their discoverers: Ludwig Schlafli and Edmund Hess. Each is represented by a Schlafli symbol in which one of the numbers is 5/2. They are thus analogous to the regular nonconvex Kepler-Poinsot polyhedra. Allowing for regular star polygons as faces, edge figures and vertex figures, these 10 polychora add to the set of six regular convex 4-polytopes. All may be derived as stellations of the 120-cell or the 600-cell.

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