 Being a covering graph of "K"4 means that there is a mathematical subgroup of symmetries of the Laves graph such that, when vertices that are symmetric to each other in this subgroup are collected together into orbits of the subgroup, there are four orbits, and each pair of orbits is connected by edges of the graph to each other one.That is, the graph whose vertices are orbits and whose edges are adjacent pairs of orbits is exactly "K"4.Being an abelian covering graph means that this subgroup of symmetries is an abelian group (in this case, the group formula_3 formed by addition of three-dimensional integer vectors), and being a maximal abelian covering graph means that there is no other covering graph of "K"4 involving a higher-dimensional abelian group.