Figure 2 in that article, illustrating a constant-width figure with three sides (a Reuleaux triangle), reminded me of a science fiction story from long ago. I finally found the title: it's "The Three-Cornered Wheel" by Poul Anderson. A spaceship crew on an alien planet needs to transport something heavy but the natives worship circles and won't let them use cylindrical rollers. They eventually find a solution that satisfies everyone.