This research investigates the design, fabrication, and structural performance of triply periodic minimal surface concrete units. The main goal is to design a unit with the least amount of concrete to be used as a building block for high-performance, low-carbon and efficient structures. Three dimensional graphic statics was used as a design tool along with robotic hot wire cutter and computer vision for fabrication. In total three units, P. Schwarz, Gyroid and a Hybrid, were built and tested experimentally and numerically. The dimensions of each minimal surface units are 30.48 x 30.48 x 30.48 cm (1' x 1' x 1'), with half an inch concrete shell confined between extrudes and intrudes foam. The formwork was built in multiple segments to lower material use. Results showed all units perform very well under the compression which reveals the potential of using these units in building walls, foundation or columns. The FE models accurately simulated the stress distributions, with the locations of high stresses corresponding well with observed crack patterns from experimental tests, thereby validating the numerical simulations. Moreover, the analysis revealed that the P. Schwarz model exhibited significant improvements in strength when confined in multiple directions, with the maximum tensile strength increasing up to 5.5 times compared to the unconfined model.