Abstract: Given a tessellation T of the plane, a new tessellation is defined by triangulating the
tiles of T that are not triangles. The
tessellations T to consider are some
regular tessellations, a Laves tessellation, a2-uniform tessellation, and nine more tessellations. In this paper it is
discussed how the periodic tessellations defined by the irreducible
triangulations of the torus are combinatorially equivalent to tessellations of
type
Keywords and phrases: tessellation of the plane, regular tessellations, Laves tessellation, 2-uniform tessellation, periodic tessellation, irreducible triangulations of the torus.