Archimedean ice (Q379576)

The topic of this work is a specific configuration of graphs, so-called ices. They should not be confounded with cold physical objects (although some of them may play a role of the mathematical model for statistical physics properties of a real ice). Here an ice is the arrangement of arrows connecting lattice vertices in such a way that the numbers of arrows arriving to and departing from a lattice point are equal to each other. The Archimedean ice corresponds to bonds between vertices of Archimedean lattices defined via the tiling of a plane by regular polygons. The main results of the article consist of a series of theorems considering ice configurations and conditions for their mutual transformations and entropy properties for Kagome, triangular and 3.4.6.4 lattices.