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layer sequences of tessellations

Layer sequences of hyperbolic tessellations




Layer sequence of a pentagonal tessellation



Each pentagon is regular, with geodesic sides and an angle of 90� at each vertex.

The layer sequence has the generating function



and is just the walk length sequence of the following directed and edge-weighted graph, starting from the circled vertex on the left






Layer sequence of the modular tessellation



Each triangle has a cusp at infinity and an angle of 60� at the other 2 vertices.

The layer sequence has the generating function



and is just the walk length sequence of the following directed and edge-weighted graph, starting from the circled vertex on the left









by Paolo Dominici
May 11, 2000