  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.
