Trichinopoly - perhaps more widely known as Viking Knit - is a wire weaving technique that involves wrapping and looping a wire, usually around a stick-like tool such as a wooden dowel, in a particular pattern. Typically, the piece is pulled through a draw plate when finished, which decreases the diameter and increases the length while tightening and evening out pattern. See an example below:
A double knit piece in progress on a wooden dowel. 26 gauge wire, 7 ribs, 8mm tool.
The same piece pictured to the left but as a finished bracelet - after being pulled through the draw plate and with findings added. Drawn to 5mm.
Although the base pattern of viking knit is very simple, there is a wide variety of pattern aesthetics within the look and feel of the final piece depending on the following variables:
Knit count (single, double, triple)
Rib count (how many columns of loops - 4 are visible on the dowel in the above left picture)
Wire gauge (I have worked with a variety of gauges from 32 to 22)
Tool diameter (how big is the dowel or similar object the wire is wrapped around)
Draw diameter (the diameter of the smallest draw plate hole the finished piece is pulled through)
Knit density has a large impact on the structural integrity of the piece. The amber double knit bracelet pictured above is not indestructible, but fairly sturdy. As you can see in the left picture on the dowel, there isn't a ton of space between the loops nor between the ribs. When pulled through the draw plate, this results in a dense weave with relatively angular loops that look like a series of V's.
Small changes can have a big impact. Observe the two pieces here - though it's a little difficult to show in photography, the piece on the right has more "empty" space inside of the bracelet. The left piece (same as the amber bracelet at the top of the page) is very similar but a little sturdier, and the V shapes created by the loops are slightly less angular.
The difference is only the tool diameter. Both are 26 gauge wire, double knit, 7 rib, and drawn down to 5mm. But the left piece was wrapped on an 8mm dowel, and the right piece on a 12mm dowel. The extra wire required to make a circle around that bigger tool is slack that has to go somewhere as the piece is drawn down, which elongates the loops and slightly decreases the knit density. Or if you prefer to think of it another way - you can increase the empty space inside a piece by increasing the size of the tool its wrapped around to begin with.
Aesthetically speaking, the difference is wholly subjective. But something I concern myself with is durability, and while both of the pieces are relatively sturdy, but the amber piece to the left is definitely more so.
These are a collection of various "recipes" I've used in an attempt to help lay out how different looks can be achieved. In the documentation and historical examples I have seen, there has been some talk of isolated variables like knit count or number of ribs, but I have found no comprehensive discussion that leads to a sufficient understanding of how those variables all impact the end product, and what combination of them you might want to use or why.
For anyone who just wants a trichinopoly chain to buy or trade, or as a gift, this would basically just be a catalog of designs. But to another wire weaver, the comparison points should help to build an understanding of how to exercise creative control over the end product.