We apply the recently introduced flattenicity event shape variable in order to identify within the inelastic proton-proton collisions at 13 TeV the presence of events with a very extended structure of low momentum tracks filling in a quasi-isotropic way the pseudorapidity-azimuth phase space, the so-called hedgehog events. We study the distribution of flattenicity values using several state-of-the-art Monte Carlo event generators, such as Pythia 8, Herwig 7 and EPOS 4. We compare the flattenicity event shape with other event shape variables commonly used to study the structure of events, such as aplanarity, centrality, sphericity, transverse thrust and transverse spherocity. We find that flattenicity does not have a strong correlation with these event shape variables, indicating that it provides complementary information in studying the global shape of an event and could improve our understanding of the underlying physics.