Abstract
Anew series of computer programs that enumerate three-dimensional periodic embedded nets (i.e., representing crystals) is based on an algorithm that can theoretically enumerate all possible structures for all possible periodic topologies. Unlike extant programs, this algorithm employs algebraic and combinatorial machinery developed during the 1980s in combinatorial and geometric group theory and ancillary fields. This algorithm was validated by a demonstration program that found all strictly binodal periodic edge-transitive 3,4-, 3,6-, 4,4-, and 4,6-coordinated nets listed in the RCSR database. These programs could be used in two ways: to suggest new ways for targeting known nets, and to provide blueprints for new chemically feasible nets. They rely on a discrete version of "turtle geometry" adapted for these nets.