Drilling Square Holes at Linearly Independent. All about the Reuleaux triangle and rotations thereof.

[I]t has the same maximum width regardless of how it is rotated. this property was thought to be only possessed by circles once and yet here’s a simple and apt counter example.

Constant width shapes can make great manhole covers, as no orientation of the cover will let it fall through the manhole. A few years ago Microsoft interviewers asked job applicants why manhole covers were round and this was thought to be one of the best answers.
Another more important property of constant width shapes is that they can rotate inside parallel lines.