Amalgamation of Regular Incidence-polytopes
نویسنده
چکیده
We discuss the following problem from the theory of regular incidence-polytopes. Given two regular d-incidence-polytopes 9X and !?2 such that the facets of 0>2 °d the vertex-figures of 0\ are isomorphic to some regular (d l)-incidence-polytope 3C, is there a regular (d +1)incidence-polytope X with facets of type ^ and vertex-figures of type &•?. Such amalgamations X of 0\ and 0*2 along 3iT exist (and then in fact very small ones) at least under the assumption that 0>, and 9*2 have the so-called degenerate amalgamation property with respect to 3if. We prove some results on preassigning the (d l)-dimensional medial section-complex 3if for self-dual (d + l)-dimensional regular incidence-polytopes X.
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