On the subject of constant-width sections, it is worth noting that a 90 degree V-block will not always detect this deviation from roundness. For example, a 7-sided constant width section will show zero deviation in a 90 degree block as measured vertically above the V. (If you doubt this, those in the UK can try it with a 50p piece.) A similar false pass will apparently be recorded by shapes with 9, 15 or 17 undulations, though I haven't tried this.
There is in fact a British Standard setting out in great detail the tests required to establish roundness (BS 3730, 1987, if you are interested). You may need to use several V-blocks of different included angle to establish true roundness, though a block of 72 degrees will work for all symmetries up to and including 18.
There is an infinite family of constant-width shapes, of which the symmetrical examples are only special cases.
David