InterLattice is a three-dimensional fastener-free joinery system composed solely of interlocking flat pieces. The InterLattice system is made up of vertically oriented triangular modules that connect to each other in a manner inspired by conventional brick and mortar construction, updated to take advantage of digital technologies available in an era of mass customization. Connection gaps between the triangular modules act as flexible joints, connecting the modules together while allowing for a wide range of angles between adjacent modules. With the InterLattice, double curvature in form is possible without the typical need for tiling or major alteration of module geometry. This enables material sheets to be nested and CNC cut simply and efficiently; tabs and slots are unique to their position, but the overall size of pieces remains consistent. The parametric model of InterLattice allows for control of lattice geometry and automatically updates connection conditions, paying attention to patterns and constraints within the design. Through this modeling process, CNC-ready InterLattice designs are simultaneously generated and visualized. InterLattice systems are highly flexible and have many potential applications including interior walls, self-supporting awnings, and as a part of weatherproofed exterior structures.