Lason, MichalMichalek, Mateusz2017-05-012017-05-012017-05-01201710.1080/10586458.2015.1128370https://infoscience.epfl.ch/handle/20.500.14299/136691WOS:000396782600002We answer several questions posed by Beck, Cox, Delgado, Gubeladze, Haase, Hibi, Higashitani, and Maclagan in [Cox et al. 14, Question 3.5 (1),(2), Question 3.6], [Beck et al. 15, Conjecture 3.5(a),(b)], and [Hasse et al. 07, Open question 3 (a),(b) p. 2310, Question p. 2316] by constructing a new family of non-normal very ample polytopes. These polytopes are certain segmental fibrations of unimodular graph polytopes, we explicitly compute their invariants - Hilbert function, Ehrhart polynomial, and gap vector.normal polytopevery ample polytopegraph polytopeHilbert basisgap vectorsegmental fibrationtext::journal::journal article::research article