Small examples of mosaics of combinatorial designs

We give the first example of a mosaic of three combinatorial designs with distinct parameters 2-(13,3,1), 2-(13,4,2), and 2-(13,6,5). Furthermore, we give examples of mosaics of 2-(9,3,2) designs that are not resolvable, thereby answering a question posed by M. Wiese and H. Boche. Finally, we give an example of a mosaic of projective planes of order 3 that cannot be obtained by tiling groups with difference sets.