The third rule was one of the favorite rules in the construction of Tchokwe sand drawings. A whole series of "social" monolinear plate designs representing a leopard with cubs, a design called kambava wamulivwe that represents an animal called kambava that died inside a rock, or lusona drawing called tambwe that represents a lion is composed this way. 

With the fourth rule we are able to produce many plate designs present in knotwork art, in particular, many symmetrical ones. That rule gives a large degree of freedom. We can add to a monolinear plate design any other square RG in a symmetrical or asymmetrical manner, a RG with the property b|a or even to work with the mirror curves with the corresponding properties. 

Creating a variety of monolinear plate designs opens the door to artistic creativity and play: there is an enormously large number of ways for introducing internal edge-incident and edge-perpendicular mirrors in order to preserve monolinearity. 

Together with the remarkable example example of a monolinear cross knot design, another interesting example is a complex monolinear design. Because the symmetrical version of the same design is a two-component knot design, the Celtic master constructed an almost symmetrical monolinear design by breaking symmetry. 

Another question is: what basic polyhedra appear in knotworks. In Tchokwe sand drawings we can find an infinite series of basic polyhedra yielding monolinear designs, beginning with the basic polyhedron 8^*, up to 162^*, etc. These series can also be obtained from the projections of torus knots of the form [4,b], GCD(4,b) = 1, if we convert those projections into alternating knots. The geometric construction of these basic polyhedra based on the natural pattern, the cobweb of a large spider, is easily recognized. It is a series of inscribed squares. Other similar infinite series of basic polyhedra inspired by patterns from nature, the growth patterns of certain plants, can be found in various artworks, for example in Michelangelo's plaza. It is the basic polyhedron corresponding to the torus knot [12,5] turned into an alternating knot. In the same way we can obtain different alternating knots corresponding to basic polyhedra derived from torus knots [a,b], GCD(a,b) = 1. All these basic polyhedra have the same simple geometric construction: a series of inscribed n-gons (n ³3).

In Celtic knotworks more sophisticated constructions resulting in basic polyhedra appeared. For their construction Celtic masters used friezes without digons, from which basic polyhedra were derived by identifying the opposite sides of friezes. That was done in the same manner used for creating other circular knot designs. 

After the recognition of the basic elements, tangles, of which complex periodical knotworks are composed (e.g., Celtic friezes or plane ornaments from, or laces), we can try to make some classification. From the theory of symmetry point of view, every such periodical structure can be described by its symmetry group: one of the 31 symmetry groups of bands, or one of the 80 symmetry groups of layers. For this description, friezes or plane ornaments are treated as 3-D objects, by taking into consideration the relation över-under". However, bands or layers that possess the same symmetry group can be, visually and topologically, very different. They can be composed of different generating elements repeated according the same symmetry rules. Therefore, together with the symmetry classification, we can use the classification of their "building blocks", tangles, according to knot theory criteria. From every tangle, by connecting NE and NW, and SE and SW strand, or by connecting NE and SE, and NW and SW stand, two closures of the tangle T are obtained: the numerator N(T) and denominator D(T), respectively. For example, from the Celtic tangles from the upper row we obtain the ordered pairs of alternating KLs: (2 1 2, 2 1 2), (3, 2 2), (1, 3), (8^*, 2 1 2 1 2), (2 1 1 1 2, 3#3), (2 1 1 1 2, 2 2 1 2), and (3#3, 2 1 2). Similarly, tangles with two open ends can be closed. Using the proposed classification method, different bands with the same symmetry group p121 have extended symbols (p121,3) and (p121,5), where the first part of the symbol is the symmetry group, and the other is the closure of the tangle generating the band. In order to obtain even more precise classification, instead of KLs obtained as closures, it is possible to use their projections.