A Laplace problem for a regular lattice with symmetric and asymmetric pentagonal cell and different obstacles

Abstract

Let 1 (a, b, c; α) and 2 (a, b, c; α, β) be regular lattices with the foundamental cell that are symmetric asymmetric and pentagonal like in fig.1 and fig.3. In this paper we compute the probability that a segment of variable position and constant length intersects a side of the lattices. In particular we obtain the Laplace probability.