Torus knots are beautiful knots formed by wrapping a line around a torus and tying the ends together to form a loop. The resulting knot has a star-like appearance when viewed from above. The 36 examples with the least number of crossings can be seen at the Knot Atlas's page on torus knots.
Just as in Tuesday's post on making knot sculptures, today's post is going to explore how to make these knots using flexible copper tubing and solid solder wire. Here's a couple of pictures showing the torus knots I've made in the last couple of days. The ones in the first picture are 1/8 inch diameter solid solder wire, and the ones in the second are 1/8 inch copper tubing with solid solder wire wrapped around the copper.
Since the torus knots are made by connecting up points on a torus in a symmetrical fashion, they look a lot like regular stars which are made by connecting up the points on a circle in the same way. I strongly suggest watching this video by Vi Hart on doodling stars. It helped me a lot when thinking about these knots.
- Solid core solder wire (get "Lead Free" so you don't worry about lead poisoning)
- Small soldering iron (you don't want the iron to get too hot or it will melt your knot)
- Copper tubing (smaller diameters are easier to bend and less likely to "krink")
- Shears to cut the copper tubing (a hacksaw would probably work well, also)
- Small round objects to help you bend smoothly (pens of various sizes work great)
- Knot diagrams to use as inspiration, or at least classification after you make a knot
Probably the easiest way to form a torus knot is to just choose a knot at the Knot Atlas's page on torus knots. The first number describing the knot is the polygon it is based on. For instance, if it has the number 7, then it is based on a heptagon, a regular seven sided figure. The second number tells you the number of points on the polygon you move when you wrap around the torus once in the short dimension. The two numbers must not share a common factor or else it would have to be formed from multiple links. This is why there are no 6,x torus knots.
Look at the knot carefully and perhaps even print out or draw the polygon the figure is based off of. Cut the wire to length making sure to leave it longer than you need, since it is hard to add length if you need it. Form the torus knot, trim to length, and connect the two ends together. Move the lobes around until you form it into a pleasing shape.
Here's a couple of pictures showing the process with a 7,2 knot made from copper wire with solder twisted around it.
Make a couple of loops:
Form them into the first pass around the long dimension of your torus knot:
On the next passes, the wire has to be wrapped through the previous ones. You can use them as a guide. Just imagine that it does exactly what the wire ahead of it does only 1 point sooner.
The knot is finished. Just have to cut the excess wire.
After making it a little more symmetrical, here's the finished knot:
When forming the knots by eye, it can be difficult to place the wire correctly and involves quite a bit of trial and error. A template can help with this and make the process faster. There is a major catch, though. The only way to remove the template is to cut it. I imagine that there are lots of possible ways to make a template. One idea I had was to buy a styrofoam torus at a craft store and dissolve the template by dipping it in gasoline. I think that this would work, but I just ended up making a template out of paper and cutting it into pieces to remove it.
Here's a few pictures showing the process of making a 9,4 torus knot with a template:
One end is taped to the template and the first few coils have been made forming the first pass around the torus. This knot will take 4 passes to complete.
More passes around the torus:
The ends meet:
After cutting the excess wire and joining the ends by wrapping them around each other and removing the template, here's the finished product:
If you build any of torus knots, let us know by posting a picture or video up on the corkboard. If you have any ideas of how to make these better or faster, be sure to comment. If you would like a copy of the template for making the 9,4 knot, send me a message onsite. I haven't had the chance to make it more user friendly yet, but I would if someone wants it.