In our previous work, a monoclinic octahedron model based on the tetragonal octahedron model for the negative compressibility property was analyzed. To design a larger number of new models with greater negative compressibility property, an extensive study to propose the hexagonal and trigonal models constructed by a hinging wine-rack mechanism is now conducted, according to the concept of the crystal system and the method to design new models by changing the system of models. The compressibility properties through theoretical modeling are analyzed, and the results show that the two models exhibit negative compressibility. Further analysis indicates that the two models have strong similarity with the tetragonal model, which can be analyzed uniformly, and the trigonal model has the greatest negative compressibility property among the three models, irrespective of the on-axis or off-axis compressibility property. Finally, owing to the particularity of the space configuration for the hexagonal and trigonal models, a series of new models with different spatial arrangements are proposed, which can greatly increase the number of models with negative compressibility.