Distance sequences in infinite regular tessellations Original Research Article

We give formulae which yield linear algorithms for calculating distance sequences in Euclidean and hyperbolic tessellations. Then, we characterize the Euclidean tessellations as the regular tessellations whose distance sequence is linear and show that, in a hyperbolic or Euclidean tessellation {p, q}, for every n > 0, q divides the circumference of the circles of radius n.