Reuleaux Triangle Ring - a "triangle" that is 100 mm wide in every direction

Draw an equilateral triangle, then replace each side with an arc centred on the opposite corner. The result is a Reuleaux triangle: a curve of constant width. Measure it with calipers at any angle and you get the same number; roll it between two parallel rulers and they never move apart.

Maths fact: of all shapes with a given constant width, the Reuleaux triangle has the smallest area (the Blaschke-Lebesgue theorem).

This ring is 100 mm wide (outer width checked in the file at every degree: 99.997 to 100.000 mm), 20 mm tall, with a 3 mm wall. It prints flat with no supports, quickly and with little filament.

Files
- reuleaux-ring-100mm.stl - the ring
- reference/reuleaux-100mm-solid.stl - the full solid disc version
- reference/reuleaux-100mm-outline.svg - the 100 mm outline at 1:1, for laser cutting or drawing

Tested: printed in PLA; the print measures 100 mm across in every direction (October 2026).

Made with Curiosa Tools - curiosa.tools

**Print settings:** PLA · 0.2 mm · flat side down · no supports · walls: let the slicer fill the 3 mm wall (perimeters) or 15-20 % infill. Turn elephant-foot compensation ON so the bottom edge stays at 100 mm. About 17 g and 1.5 h on a standard printer, 35-45 min fast (estimate).
**Try it:** measure the outer width at several angles at mid-height, or roll the ring between two straight edges 100 mm apart.