Abstract: An inhabitable space frame (100) can define and support inhabitable living space within, around and projecting from the exterior of the perimeter of the space frame (100). The space frame (100) includes a vector matrix of strut members (105) that defines a plurality of interconnected basic tetrahedral modules (110) and, optionally, a plurality of prime octahedral modules (115). At least a part of each prime octahedral module (115) in the plurality of prime octahedral modules (115) is adjacent to at least two of the basic tetrahedral modules (110). Use of one or more right triangular faces, or planes, within a repeating geometry of a vector matrix enables an interior of the space frame (100) to be inhabitable, with horizontal floors and vertical walls aligned with associated strut members (105).