3D Farey graph, lambda lengths and SL2-tilings
Abstract
We explore a three-dimensional counterpart of the Farey tessellation and its relations to Penner's lambda lengths and SL2-tilings. In particular, we prove a three-dimensional version of Ptolemy relation, and generalise results of Ian Short to classify tame SL2-tilings over Eisenstein integers in terms of pairs of paths in the 3D Farey graph.
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