To expand search, see Symmetry. Laterally related topics: Frieze Patterns, Plane Patterns, Bichromatic Strip Patterns, Five Fold Symmetry, Penrose Tilings, Pattern, The Regular Solids, Double Frieze Patterns, Rotational Symmetry Groups (Rosettes), Bichromatic Plane Patterns, and Dynamic Symmetry.
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Cromwell, Peter R. Celtic knotwork: mathematical art. Math. Intelligencer 15 (1993), no. 1, 36--47. SC: 01A07 (00A69), MR: 1 199 275.
Cromwell discusses a theory for the construction of Celtic knot friezes. These knot patterns may have been inspired by basketry (or maybe by textiles). He then analyzes the patterns in the knot friezes using a notion of a two-sided frieze pattern. There turn out to be 31 such patterns; 7 of these are the standard monochromatic strip patterns; 17 are exactly analogous to the bichromatic strip patterns; and 7 are like the monochromatic strip patterns but require the two sides to be identical. These last 7 "grey" patterns can't occur in knotwork, since the two sides of a crossing are not identical. Of the 24 monochromatic and bichromatic patterns, 12 cannot occur in Celtic knotwork because they would require strings that don't tie up, and 2 require a string straight through the centerline (and also don't occur). The other 10 can theoretically appear. Of these 10, two do not seem to occur at all, and one occurs but with an apparently different constriction technique (an example of this type is thought to be Scandinavian). The author is able to explain the rareness of these symmetry types in terms of the theory for their construction and from the fact that Celtic know friezes were generally finite and had their ends knotted together; these constraints require construction with an even grid, and the three problematic patterns require construction with an odd grid. This explains the type which does occur appears to use a different construction technique. In fact, the author found only one Celtic pattern that uses an odd grid. (And of course it can't be used in a bounded way, though it can be used in a kind of border.) All 7 of the monochromatic frieze patterns were apparently used in generating the existing know patterns, assuming the theory of construction is true (the author makes no claims that it is). The author includes examples of his own for the 3 problematic odd-grid know patterns. Excellent article. The author includes a good bibliography of related topics. It goes as far as Norwegian peasant art, for example. Not inordinately technical, in spite of the way it might sound. Closely related topics: The Celts, Knots and Knotwork, Frieze Patterns, Bichromatic Strip Patterns, Weaving, and Basket Making.