Object of Constant Width - Reuleaux Pentagon

I have two other Reuleaux shapes on here, the more common triangle shape. But a Reuleaux can be made for any odd-number N-gon, meaning triangle, pentagon, septagon, etc.

The easiest way to make one is with the revolve, as seen in this shape. You just build a Reuleaux-correct 2d shape and then 360° revolve it.

With the pentagon version, it looks even more bizarre than the Reuleaux triangle, it looks like it *shouldn't work*. There's some kind of optical illusion in the way out brain process