The set is essentially formed of parallelepipedic base pieces (1) with a perimetric groove in the edge thereof for inserting tongues (3) projecting from some of the edges. They are provided with at least one axial opening (4) which receives another piece embodied by a stepped cylindrical button (5) which may rotate in its housing due to the presence of four axial peripheral lugs (7) which are housed into an annular undercut (6) of the base piece (1), said undercut being concentric with respect to the opening. Both the annular undercuts (6) and the axial lugs (7) are provided on both sides of the piece. The cylindrical button (5) has a diametral groove (9) which is open at the periphery. Other triangular pieces (13, 14) are also provided by cutting diagonally the square base pieces (1), having protuberances (15) and recesses (16) for interconnection purposes. The set also includes hinge-type articulated pieces (17) of which the wings are similar to the square base pieces (1). There are also covers (19) which are nestable between each other and into the axial opening (4) by means of the annular undercut (6) of any other piece; there are also triangular covers (20) acting as half-elements. By using the base pieces (1) it is possible to form on a board mosaic drawings with the square (19) and triangular (20) covers.