Triply Poly Minimal Surfaces (TPMS) are three dimensional periodic lattice structures with a trigonometric relationship in their unit cell that can be implemented for acoustic applications including acoustic metamaterials and Phononic crystals. The necessity and demand in the ultrasound and acoustic industry for new materials pave the way to investigate further mechanical wave research into the different shape of engineered metamaterials that usually does not exist in nature for different purposes. This paper presents a design pipeline for Schwarz Primitive acoustic metamaterial from the mathematically driven stage of computational design of the unit cell with the utilization of finite element method to simulate the Phononic bandgaps, acoustic pressure, wave propagations, sound pressure levels, and sound transmission loss. The effect of periodic, Floquet, symmetry, & dipole boundary conditions as well as the effect of the upstream and downstream numerical domain extension on the final transmission loss signal in the simulations are compared. These numerical evaluations are important for future experimental acoustic measurement in the different impedance tubes with different microphone positions and sample setups. Finally, the initial stage of additive manufacturing using Stereolithography 3D printing technology for the fabrication of TPMS sample to compare the numerical data with experimental acoustic data is addressed as well as its potential applications to use in the different industries.