I'm working on an app which generates 3D models of Turk's head knots which can then be 3D printed. I thought it would be cool to generate Turk's head dice, so I went about making it happen!
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Step 1: Design
This is a tool I wrote which allows you to design Turk's head knots on a knot grid: http://freakinsweetapps.com/knots/knotgrid/advanced.html
Using that tool, I designed the knot that would work as a die, which is the image above. If you'd like to see the knot in the tool above you can copy the contents of this file into the Save/Load text box at the bottom: http://freakinsweetapps.com/knots/die.txt
Step 2: Prototype
I was pretty sure that knot would nicely cover a cube, but I needed to give it a shot. I added some lines to the knot which I could cut along and fold to form it into a cube. It all fit together perfectly!
Step 3: Implement
Next, I implemented the mapping from the flat grid to a 3D cube. Here are renders from my app.
Step 4: 3D Print
I had it 3D printed through Shapeways, check it out!
This one is about the size of a real die, which is so small a lot of the detail was lost:
This one is a little bigger than a 2" cube, but you can see the weave pattern very well! http://www.shapeways.com/model/1162426/large-turk-s-head-die.html