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In three dimensions there are four Kepler–Poinsot polyhedra, and in four dimensions ten Schläfli–Hess polychora; in higher dimensions there are no non-convex regular figures.
A Schläfli symbol is closely related to reflection symmetry groups, also called Coxeter groups, given with the same indices, but square brackets instead p,q,r,....
The ones that have include the 10 regular nonconvex polychora (Schläfli-Hess polychora) and 57 prisms on the nonconvex uniform polyhedra, as well as three infinite families: the prisms on the star antiprisms, the duoprisms formed by multiplying two star polygons, and the duoprisms formed by multiplying an ordinary polygon with a star polygon.