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Wednesday, June 11, 2014

Day 289 - Braid representation of 7_2

Continuing with the knot conformations series we started on Day 266, today we printed a braid representation of the knot 7_2.

Thingiverse link: http://www.thingiverse.com/make:82269

Settings: Printed on a Replicator 2 with our custom knot support profile.

Technical notes, Mathematica/Blender/Tinkercad flavor: This knot was printed by JMU student Patrick Moran, using Mathematica to get the original braid shape, Blender to thicken the strands, and Tinkercad to add bars at the top and bottom of the model. Here is what he has to say about his process:

For the knot 7_6 I decided to show a simple braid representation, where the crossings occur between adjacent strands in a series of strands that we imagine as connecting up at the ends (that is, the first strand at the top bar is connected to the first strand on the bottom bar, and so on). Every knot has such a braid representation; see Colin Adams' Knot Book for a nice proof of this. To get a 3D model of the braid representation I used Mathematica, with commands as shown in this screenshot:

After exporting we used the Blender-thickening method from Day 285 to thicken the strands, and added bars to the top and bottom using Tinkercad.