The tessellating elements are in sets and comprise (a) at least one curve element comprising a semi-circle of diameter x; (b) at least one wave element having a perimeter which is three-sided, including a first side which is straight and of length x, a second side which comprises a concave curve forming a semi-circle of diameter x, and a third side which comprises a convex curve forming a quarter circle of radius x; (c) at least one corner element having a perimeter which is three-sided, including two sides of length x at right angles to one another and a third side which is concave and comprises a quarter circle of radius x; and, optionally, (d) one or more lozenge elements having at least one shaped face with a perimeter comprising two arcuate edges, each said arcuate edge having a radius of curvature x. The elements have a wide range of applications, from building tiles and children's toys, to screen-filling of computer screens or the like. In use, the elements are laid on a surface in a space-filling manner with straight edges abutting straight edges of adjacent elements, and convex curved edges abutting concave curved edges of adjacent elements.