Non-normal very ample polytopes - constructions and examples

We present a method of constructing non-normal very ample polytopes as a segmental fibration of unimodular graph polytopes. In many cases we explicitly compute their invariants - Hilbert function, Ehrhart polynomial, gap vector. In particular, we answer several questions posed by Beck, Cox, Delgado, Gubeladze, Haase, Hibi, Higashitani and Maclagan.