Chiral metastructures consisting of ring (polygonal or cubic) nodes and elastic bending ligaments exhibit excellent design flexibility for compliant structures. In this paper, based on rigid cubic node rotation and the kinematic geometrical relations of a three-dimensional (3D) isotropic anti-tetrachiral structure, an analytical expression for the modulus of the 3D isotropic anti-tetrachiral structure is derived from strain energy analysis. The nylon powder Selected Laser Sintering (SLS) additive manufacturing technique is employed for fabricating two types of 3D isotropic anti-tetrachiral specimens with different geometrical parameters; then comparison between experiments, finite element analysis (FEA), and theoretical studies is performed for verifying the analytical formula. The mechanical properties of 3D isotropic anti-tetrachiral structures can be tuned with two independent dimensionless geometrical parameters. The proposed 3D anti-tetrachiral structures can be employed for designing advanced structures against impact damages, realizing flexibility of industrial components, and optimizing the vibration attenuation abilities of engineering structures.