Twisted Treasures: Tetrahedral Knots

Discover the enchanting allure of Twisted Treasure, a fusion of art and advanced geometry. This unique design highlights chiral tetrahedral symmetry, weaving intricate paths into a harmonious structure that challenges perceptions and captivates the eye. Perfectly balanced and endlessly fascinating, this knot is a beautiful piece of geometric art.

To ensure the best results, this model includes customized supports in the slicer profile for flawless 3D printing, as show. An additional version included here allows you to display it as a hanging ornament, making it a versatile piece for seasonal decor or year-round sophistication. Whether showcased on a shelf, desk, or as part of your creative space, Twisted Treasure adds an element of wonder to any setting.  I also provide a super-sized version in the profile, but I have not tested this large one.  If you use this or a scaled version, please see the printing notes below!

This design draws  from the Klein Map Dual, as described in Egon Schulte and Jörg M. Wills’ paper, “A Polyhedral Realization of Felix Klein’s Map {3,7}_8 on a Riemann Surface of Genus 3” (Journal of the London Mathematical Society, 32, 1985). It’s a tribute to the intersection of mathematics and art, brought to life through precise 3D printing. Let Twisted Treasure: The Tetrahedral Knot spark conversation, admiration, and a deeper appreciation for the beauty of geometry. It’s not just a sculpture—it’s a masterpiece waiting to be part of your world!

Printing:

First, make sure your build plate is clean/you've got a good grip with your filament.  Consider using glue, as the connected area on the base plate is low for a large portion of the print.

The custom supports in the prearranged file here are important for a good result.  Printing them as a regular object and using organic tree supports on them should end up looking like this:

Note that the gap between the very thin line to guide the organic supports and the actual model is very small (1 layer height @0.12 mm layer height) , but it will be easy to remove after printing because of the very small contact surface:

If you adjust the layer height to a value other than 0.12 mm I strongly suggest you carefully inspect the supports to make sure they look suitable for your print.

Assembly:

For the regular version, no assembly is required.  For the hang-able version, simply pop the little top onto the hole in the print with a dab of glue, and suspend with fishing wire/thread/whatever, as shown.