Based on the unique monoclinic characteristics of the plastic deformation of the tetra-missing rib honeycomb, the symmetrical design of the whole and subunits of the tetra-missing rib honeycomb was carried out in this paper, and two new types of tetra-missing rib honeycomb with symmetrical structural characteristics were obtained. First, quasi-static compression was performed on three structures, including a conventional tetra-missing rib honeycomb, and the experimental results showed that both symmetrical designs could effectively improve the plastic deformation of the conventional tetra-missing rib honeycomb. At the same time, round holes were introduced into the three honeycomb structures, and the mechanical properties and deformation modes of the three structures under quasi-static loads were explored. The results of two sets of experiments were compared, and it was found that the introduction of round holes could improve the structural stiffness of the honeycomb. Second, Abaqus/Explicit was used to construct a finite element numerical model in the later stage, and the accuracy of the model was verified. The number of honeycomb cells was determined for the three honeycomb structures, and finally, the dynamic Poisson's ratio of the honeycomb structure in plastic deformation was determined, and the negative Poisson's ratio (NPR) effect of the three honeycombs was compared.