Umbilic Torus with a Twist

thingiverse

This model demonstrates an intricate umbilic torus created in Blender using advanced geometry manipulation techniques. Starting with an equilateral triangle, it was extruded outward and then carefully deformed by pulling each side inward by exactly 50%. To add a layer of complexity, the entire shape was then scaled along its sine wave path, gradually increasing its dimensions as it followed a curved trajectory. Ultimately, the torus was twisted back onto itself, revealing an astonishing result: as it traverses 2π, this umbilic torus effortlessly rotates a full 120 degrees while undergoing periodic growth and contraction. Only the support from the 3D printing platform is necessary for bringing this design to life. Although there's a slim possibility of successfully orienting the model without requiring any supports, I did not explore that particular option in detail.