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LINEAR CELTIC KNOT
Fantasist page. 
Using the following three basic pieces:



A, and its left/right flip, that will provide a crossing,  B, and its left/right flip, that will provide two crossings,  M, that will provide three crossings, 
First examples:
TYPE AA: 1+1 = 2 crossings, Hopf link


TYPE BA: 2+1 = 3 crossings, trefoil knot 

TYPE BB: 2+2 = 4 crossings, Solomon's knot 

TYPE AMA: 1+3+1 = 5 crossings, Whitehead link 

TYPE BMA: 2+3+1 = 6 crossings, knot 6.1.2 

TYPE BMB: 2+3+2 = 7 crossings, knot 7.1.4 

TYPE AM^{2}A: 1+6+1 = 8 crossings, link 8.2.7 

TYPE BM^{2}A: 2+6+1 = 9 crossings, knot 9.1.20 

TYPE BM^{2}B: 2+6+2 = 10 crossings, link L10a101 

Small theorem: the BM^{n}A always are knots, the AM^{n}A always have two blades, and the BM^{n}B, which are rectangular billiard knots of the type (n+2, 2), are knots for odd values of n, and have two blades otherwise.
This Wehrmacht officer's epaulette (see here) is a BM^{3}A; knot
K12a541
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© Robert FERRÉOL 2018