Monohedrons
27/01/2024
Monohedrons: solids with a single edge (and thus a single face). There are infinitely many: simply rotate a polygon in a plane of revolution while spinning it on its center by 2pi/n, where n is the number of sides.
Here’s an example (made with a 3D printer) for n=3:
Another monohedron example, CAD-modeled, for n=6:
Since the limit figure of an n-sided polygon as n approaches infinity is a circle, the ultimate monohedron is a torus, still with one face but no edges :-)
Note: numerunique always creates objects from a blank page, then checks for similar ones. In this case, there’s an example of a monohedron with a square section, already published by Jean-Pierre Petit!
Update: A chance encounter revealed these "monohedrons" are special cases of rotoids. Confirming, if needed, that search engines omit the most interesting sources.