Distance sequences in infinite regular tessellations (Q1903731)

The author gives formulae for calculating distance sequences in hyperbolic and Euclidean tessellation and uses them to characterize the Euclidean tessellation as the regular tessellation whose distance sequence is linear. For hyperbolic tessellations \(\{p,q\}\), the author shows that \(q\) divides the circumference \(c_n\) of the circles of radius \(n\).