Circular arc rotors

Start wih a regular pentagon. All the arcs are circular, centred at the vertex of the polgon. There are larger and smaller arcs, the lengths of which ensure the shape is closed.

The result is a shape of constant width.

You can manipulate the blue points. But R is restricted to one arc. You have to appeal to symmetry for the rest!

Chris Sangwin, 9 Feb 2007, Created with GeoGebra