An auxetic metamaterial based on a semirotation system is designed herein by combining rigid units of two different shapes, such that each unit cell consists of one nonrotating rhombus and four rotating right triangles. The on‐axes Poisson's ratios are obtained for both infinitesimal and finite deformations by geometrical consideration. The on‐axes Young's moduli of this metamaterial are established by matching the spring potential energy stored at the hinged joints with the strain energy of deformation for the homogenized continuum of the metamaterial. Plotted results describe the interlacing effect of the shape descriptor, the original separation angles, and the change in the separation angle on the on‐axes Poisson's ratio and Young's modulus. The latter is directly proportional to the equivalent spring stiffness per unit cell. In addition to attaining auxetic behavior, this metamaterial can also be designed to achieve specific Young's modulus behavior including extreme stiffness in one of the directions either at infinitesimal or finite deformation. This Aztec‐inspired metamaterial exhibits auxetic behavior for the shown range via rotating triangles and nonrotating rhombi as a result of on‐axes loading. In terms of area, 50% of the metamaterial is nonrotating.