Mathematical Art: The Inverted Oloid

Overview

This model is a unique take on the Oloid, a three-dimensional curved geometric object discovered by Paul Schatz in 1929. Unlike a standard solid oloid, this inverted oloid features a hollowed-out center that emphasizes the mesmerizing, continuous surface and complex geometry.

It is more than just a sculpture; it is a tactile "fidget" desk toy and a sophisticated conversation piece. Its unique shape allows it to roll in a peculiar, wobbling motion, and it develops an incredibly complex shadow profile under direct light.

Design Details

• Source: Developed as a custom design.

• Software: Modeled with precision in FreeCAD.

• Geometry: Derived from the convex hull of two linked congruent circles in perpendicular planes, then inverted to reveal its inner architecture.

Recommended Print Settings

To capture the smooth transitions of these steep curves, I recommend the following:

• Filament: Matte Grey PLA (as shown in the renders) or Silk PLA for a metallic look.

• Layer Height: 0.12mm or 0.16mm for the best surface finish on the curves.

• Walls/Perimeters: 3 walls for structural integrity.

• Infill: 10-15% (Gyroid works well for geometric models).

• Supports: Minimal supports may be required depending on your printer’s cooling and bridging performance.

• Orientation: For the smoothest finish, print it resting on one of its curved edges with a small brim for stability.

How to video

https://m.youtube.com/watch?v=3P29Ljokl_I