Let us now describe four general rules for combining plate designs and/or mirror curves. The first three of these rules are given by P. Gerdes (1999), and the fourth is proposed by S. Jablan. We will restrict our consideration to mirror curves placed in polyominoes with square cells. The first rule defines a combination of two mirror curves that share one edge of an open cell on their borders. Such a composition corresponds to the direct product of KLs, and it was probably one of the most exploited constructions in knotwork art. For given mirror curves M_{1} and M_{2}, this kind of direct product we will call ×direct product and denote it by M_{1}×M_{2}. If we combine two mirror curves in this way, first with c_{1}, and the other with c_{2} components, the result is a new mirror curve with c_{1}+c_{2}1 components. Hence, the ×direct product of two 1component mirror curves is a new 1component mirror curve. This idea was used, for example, in the Tchokwe designs and in many Celtic friezes. As a particular application of the first rule, we can add a single square to the border of any monolinear mirror curve. This transformation is the addition of an external loop. It does not change the number of components and can be repeated as many times you like. For example, the Tamil (unknot) design is created by a series of external loop additions, beginning from the RG[1,1]; the other knot design by adding loops to the RG[4,3]; and the third knot design by adding loops to the RG[5,3]. The same construction is used for Tchokwe designs. In knotwork art it has a decorative function. The second rule is exactly the one by which we define the direct product K_{1}#K_{2} of two knots K_{1} and K_{2} in knot theory. In the language of mirror curves M_{1} and M_{2}, it means that we cut one external edge of each mirrorcurve M_{1} and M_{2}, and reconnect them again to obtain a new mirrorcurve, that will be denoted by M_{1}M_{2}. The third rule is restricted to plate designs: two monolinear plate designs whose overlapping contains exactly two cells will give a new monolinear plate design. The schematic interpretation of the third rule is given in the corresponding figure. In order to introduce the fourth rule we need a new operation, addition. The addition of a plate design P_{1} to plate design P_{2} is an edgetoedge identification of their border cells belonging to rectilinear borders. In the same way, we can add a plate design P_{1} to some mirror curve M placed in some polyomino. The fourth rule is: an RG[a,b] for which ba, added to any monolinear mirror curve M (or monolinear plate design P_{2}) incident to it along the edge b, will give a monolinear design. In particular, any square RG added to a monolinear design gives a new monolinear design. Rule 4 can be also applied to mirror curves. In this case, we can add a mirror curve M_{2} to a monolinear mirror curve M_{1}, that every point of an edge b of the polyomino in which M_{2} is placed belongs to a different component of M_{2}. The new mirror curve M_{1}+M_{2} will be monolinear. By using the four rules mentioned we are able to produce monolinear plate designs and extend the monolinearity property from RGs to plate designs.
