3D-printed Conformations of Knots through 7 Crossings

Description

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 knot 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: 

0_1 at Day 267

3_1 at Day 268 

4_1 at Day 269 

5_1 at Day 272 

5_2 at Day 273 

6_1 at Day 275 

6_2 at Day 276 

6_3 at Day 285 

7_1 at Day 286 

7_2 at Day 289 

7_3 at Day 290 

7_4 at Day 291 

7_5 at Day 295 

7_6 at Day 296 

7_7 at Day 299

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Twitter:  twitter.com/mathgrrl

Hacktastic blog:  www.mathgrrl.com/hacktastic

Shapeways geekhaus store:  www.shapeways.com/shops/mathgr... 

This design and all associated pictures and files are licensed under the Creative Commons Attribution Non-Commercial Share Alike license. If you want to use designs, images, or files outside of the terms of this license, please email [email protected]

Design Files

File Size

7_4_Pretzel.stl
1.63 MB
7_7_part1_blue.stl
385 KB
7_7_part2_green.stl
418 KB
7_1_Bone.stl
1.17 MB
7_3_Bone.stl
1.52 MB
6_1_Bone.stl
1.19 MB
7_5_Tangle.stl
253 KB
5_1_Lattice.stl
438 KB
6_3_Seifert.stl
834 KB
7_2_Braid.stl
695 KB
6_2_Bone.stl
1.02 MB
7_7_part5_red.stl
817 KB
7_7_Bone.stl
1.13 MB
7_7_part4_red.stl
470 KB
7_7_part3_blue.stl
328 KB
7_6_part6_green.stl
186 KB
7_2_Bone.stl
1.07 MB
6_3_Bone.stl
1.06 MB
7_6_Bone.stl
1.27 MB
7_5_Bone.stl
1.22 MB
7_4_Bone.stl
1.27 MB
7_6_Spiral.stl
6.05 MB
4_1_Bone.stl
880 KB
7_1_Torus.stl
8.57 MB
6_2_Petal.stl
5.67 MB
5_2_Bone.stl
1.01 MB
3_1_Bone.stl
601 KB
5_1_Bone.stl
879 KB
3_1_Tritangentless.stl
1.55 MB
0_1_Crazy.stl
5.48 MB
0_1_Bone.stl
537 KB
7_3_Cantarella.stl
375 KB
6_1_Mosaic.stl
993 KB
5_2_Lissajous.stl
2.02 MB
4_1_Stick.stl
336 KB

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