Periodic Steiner Networks Minimizing Length
Jerome Alex, Karsten Große-Brauckmann · Discrete & Computational Geometry · 2023
Abstract We study a problem of geometric graph theory: We determine the triply periodic graph in Euclidean 3-space which minimizes length among all graphs spanning a fundamental domain with the same volume. The minimizer is the so-called network with quotient the complete graph on four vertices $$K_4$$ K 4 . For comparison we consider a competing topological class, also with a quotient on four vertices, and determine the minimizing networks.