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Prolong Knot Chains

Counting the crossings with these, for pricing purposes, can be a little confusing. It works out to five crossings per edge loop, plus three more at the end, so the three-loop knot has 3x5+3, or 18 crossings, and the ten-loop knot has 10x5+3, or 53 crossings. When interlinked, each knot crosses one of its neighbors at each loop, so a linked chain has the total crossings within each knot, plus the intersecting crossings between knots. The bracelets pictured here each have twenty links, so their total crossings would be, for the narrow silver chain, 20x9=180, for the wide silver chain, 20x63=1260, and for the gold, 20x21=420. Here's a schedule that may make it clearer:
Complexity of Single-Line Prolong Knot Chain, per link:
Loops Crossings
1 9
3 21
4 27
6 39
7 45
9 57
10 63

Knotted Chain Mail

Currently this involves one particular knot, a 3x4 Turk's Head with eight internal crossings and four external ones. The external crossings are held in common with other knots.
Complexity of Knotted Chain Mail, per link:
LxB Crossings
3x4 12

Turk's Head Knot Chains

Chains made with interlinked Turk's Heads are orders of magnitude more difficult and complex, so the labor cost is much greater. There is only one such chain in existence at this time, the 5x6 chain that I made back in 2000.
Complexity of Single-Line Turk's Head Knot Chain, per link:
LxB Crossings
5x6 30
5x7 35
5x8 40

(This site last updated on 12-11-2017)

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