This work describes the behavior of a novel class of hierarchical slotted and asymmetrical edge cellular shapes honeycombs with auxetic and non-auxetic configurations subjected to edgewise compression. Hierarchical (slotted) and non-hierarchical specimens including hexagonal, re-entrant and asymmetric re-entrant have been 3D printed by using PLA plastic and tested under edgewise compression along the in-plane directions. The material properties of the PLA plastics have been determined via tensile tests, and Finite Element analyses have been performed using the LS-DYNA code to benchmark force-displacement curves with the experimental results. The numerical models were validated by comparing the load-displacement responses with the experimental results for each sample. Linear elastic properties, crashworthiness and energy absorption capability of the novel honeycomb structures are evaluated from the experimental and numerical standpoint. Specific metrics like compressive normalized modulus, compressive strength and specific energy absorption (SEA) are evaluated. The Poisson's ratio of the novel honeycomb configurations has been evaluated and the impact of the deformation mechanisms of the different cellular shapes during crashworthiness has been studied. The results show that the use of the slotted and asymmetric cells proposed in this work could increase strength, stiffness and energy absorption capacity and also increase the stability of the samples during deformation.