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Friday, January 10, 2014

Day 137 - Clover knot

More TopMod! Today we made a knot:


STL file: http://www.geekhaus.com/makerhome/day137_cloverknot.stl
Thingiverse link: http://www.thingiverse.com/thing:224032

Settings: MakerWare .15mm/high with raft and supports, in 6 hours and 23 minutes. I didn't use the custom knot supports from Day 110 because sometimes they don't work well for thin knots. The supports were not as much of a pain to remove as I thought they would be, and somehow we managed to do so without breaking the model!

Technical notes, math flavor: This model is an example of a mathematical knot, which is basically a string in space that is tied up and then spliced together at the end to make a knotted loop. But which knot is this? It might even be the unknot! Later this semester I'll give this to a student to figure that out. A good place to start would be by making a knot diagram and computing a simple invariant like the knot determinant. With a little luck that could completely determine the knot type, but if not then there are other things that we can look at. Stay tuned for an update when we figure out which knot it is.

Technical notes, TopMod flavor: This model was made by starting with a cube and then adding handles to adjacent faces, just as we did in Day 135, but this time with a twist. Literally, that is: we set "extra twists" to "1" in the properties box before we made the handles.  Then we selected some complements of face loops and used rind modeling to create crusts, and applied Doo-Sabin remeshing to soften the hard edges, just as we did in Day 136. So nothing new here, except that we figured out that you can select some individual mesh cells before beginning the face-loop selection so that there aren't holes to fill in later as we had yesterday in Step 4. The only tricky part was getting the initial twisty handles attached correctly in the first place, with the right amount and direction of twistiness.

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