  Every regular polytope has the remarkable property that it inherits all
symmetries of each of its facets. This property distinguishes a natural class
of polytopes which are called hereditary. Regular polytopes are by definition
hereditary, but the other polytopes in this class are interesting, have
possible applications in modeling of structures, and have not been previously
investigated. This paper establishes the basic theory of hereditary polytopes,
focussing on the analysis and construction of hereditary polytopes with highly
symmetric faces.
