Isoperimetric robots are large scale, untethered inflatable robots that can undergo large shape changes, but have only been demonstrated in one 3D shape -- an octahedron. These robots consist of independent triangles that can change shape while maintaining their perimeter by moving the relative position of their joints. We introduce an optimization routine that determines if an arbitrary graph can be partitioned into unique triangles, and thus be constructed as an isoperimetric robotic system. We enumerate all minimally rigid graphs that can be constructed with unique triangles up to 9 nodes (7 triangles), and characterize the workspace of one node of each these robots. We also present a method for constructing larger graphs that can be partitioned by assembling subgraphs that are already partitioned into triangles. This enables a wide variety of isoperimetric robot configurations.