3D-printed Conformations of Knots through 7 Crossings

3D-printed Conformations of Knots through 7 Crossings Free 3D print model

Knots are embeddings of circles in 3-dimensional space, but they are typically studied in terms of their projections into 2-dimensional space. We can use 3D printing to study knots in a more 3-dimensional way. In this series we present 3D printed conformations of the fifteen knots through seven crossings, including stick, Lissajous, lattice, torus, petal, and pretzel conformations. Constructing a 3D model that is actually printable can challenging; to 3D print the knot conformations through seven crossings, we used a combination of Mathematica, Blender, Tinkercad, Knotplot, SeifertView, and OpenSCAD. For detailed information about the mathematics and the design behind these models, see the MakerHome blog, starting with Day 266: http://makerhome.blogspot.com/2014/05/day-266-knot-conformations-series.html UPDATE: A fixed version of the STL file for the pretzel knot 7_4 (which had an incorrect center crossing) is now uploaded. UPDATE: The MakerHome blog series on these knots is now finished; see how each knot is made and what its conformation means at the links below. 0_1 at Day 267: http://makerhome.blogspot.com/2014/05/day-267-crazy-conformation-of-01.html 3_1 at Day 268: http://makerhome.blogspot.com/2014/05/day-268-tritangentless-conformation-of.html 4_1 at Day 269: http://makerhome.blogspot.com/2014/05/day-269-minimal-stick-conformation-of-41.html 5_1 at Day 272: http://makerhome.blogspot.com/2014/05/day-272-lattice-conformation-of-51.html 5_2 at Day 273: http://makerhome.blogspot.com/2014/05/day-273-lissajous-conformation-of-52.html 6_1 at Day 275: http://makerhome.blogspot.com/2014/05/day-275-mosaic-conformation-of-61.html 6_2 at Day 276: http://makerhome.blogspot.com/2014/05/day-276-petal-conformation-of-62.html 6_3 at Day 285: http://makerhome.blogspot.com/2014/06/day-285-seifert-surface-of-63.html 7_1 at Day 286: http://makerhome.blogspot.com/2014/06/day-286-torus-conformations-of-71.html 7_2 at Day 289: http://makerhome.blogspot.com/2014/06/day-289-braid-representation-of-72.html 7_3 at Day 290: http://makerhome.blogspot.com/2014/06/day-290-cantarella-conformation-of-73.html 7_4 at Day 291: http://makerhome.blogspot.com/2014/06/day-291-friday-fail-crossing-change.html 7_5 at Day 295: http://makerhome.blogspot.com/2014/06/day-295-tangle-conformation-of-75.html 7_6 at Day 296: http://makerhome.blogspot.com/2014/06/day-296-spiral-conformation-of-76.html 7_7 at Day 299: http://makerhome.blogspot.com/2014/06/day-299-tricolored-representation-of-77.html

M
miniqwe
thank for doing this beautiful and free work
Item rating
0 0
3D-printed Conformations of Knots through 7 Crossings
Free
 
Custom License 
3D-printed Conformations of Knots through 7 Crossings
Free
 
Custom License 
Response 0% in 48.0h

3D Model formats

Format limitations
  • Stereolithography (.stl) (33 files)50.4 MB

3D Model details

  • Publish date2014-10-10
  • Model ID#83176
Help