Torus Knot T(3,5) On Hyperboloid Surface 3D Printer Model
The file 'Torus Knot T(3,5) On Hyperboloid Surface 3D Printer Model' is (stl) file type, size is 7.9MB.
The file 'Torus Knot T(3,5) On Hyperboloid Surface 3D Printer Model' is (stl) file type, size is 7.9MB.
A T(p,q) torus knot (or link can) be constructed so the knot is polygonal and the edges lie on two distinct hyperboloids of one sheet. As the knot is traversed, the edges alternate between lying on the first then the second hyperboloid. This construction comes from Section 1.5 of the textbook Knots and Links by Peter Cromwell.
I have included three stl files: the union of the knot and the surface, the knot, and the surface without the knot. The last two files can be used to create a print where the knot is one color and the surface is a different color.
The details of how these knots were made 3D printable can be found here: https://mathvis.academic.wlu.edu/2024/08/07/hyperboloidal-representation-of-torus-knots/
An explanation of a doubly-ruled surface can be found here: https://mathvis.academic.wlu.edu/2024/08/08/doubly-ruled-surfaces/
An explanation of how the two hyperboloids of one sheet were constructed can be found here: https://mathvis.academic.wlu.edu/2024/08/14/torus-knots-on-hyperboloids-part-2/
| T53H-wH-v2-print.stl | 6.2MB | |
| T53HwH-knot-color1.stl | 6.8MB | |
| T53HwH-surface-color2.stl | 5.8MB |
