Oloid - the shape that rolls on its whole surface (print in halves + paper pattern)

The oloid is the convex hull of two equal circles set at right angles, each passing through the other's centre. Give it a push and it wobbles along a meandering path, touching the table with every point of its curved surface as it rolls.

Maths fact: its surface area is exactly 4πr², the same as a sphere of the same radius - and because the surface is developable, it unrolls flat from one piece of paper (pattern included).

This model has circle radius 30 mm (90 × 60 × 60 mm assembled). It is split on the plane of one circle, so each half prints flat-side down without supports. Glue the two halves face to face.

Files
- oloid-r30-half-A.stl, oloid-r30-half-B.stl - print one of each (each 90 × 60 × 30 mm)
- oloid-r30-flat-pattern-A4.pdf / .svg - 1:1 paper or card pattern for the same r 30 oloid
- oloid-r50-flat-pattern-A4.pdf / .svg - a larger r 50 paper oloid on A4 landscape
- reference/oloid-r30-whole.stl - the uncut solid, for viewing only (it needs supports)

Tested: printed in PLA, halves glued, rolls as described (October 2026).

Made with Curiosa Tools - curiosa.tools

**Print settings:** PLA · 0.2 mm layers · 15-20 % infill · no supports · both halves flat (cut) face down on the bed, as the files are oriented. About 16-18 g and 1.5-2 h per half on a standard printer, 35-45 min on a fast one (estimate, not slicer output).
**Assembly:** turn half B over about its long X axis and lay it on half A so the two flat faces and outlines match; glue (CA glue or PLA-safe epoxy). Light sanding of the seam if wanted.
**Paper pattern:** print at 100 % (actual size, check the 50 mm bar), cut out, curve the sheet so the edges meet and tape the joint on the inside. The pattern has no glue tabs.