I often hear that the regular simplex is "the least" symmetric convex body, and I've heard that there are some measures of symmetry of a body, that the simplex minimizes. Could you please explain or refer me to what methods / measurements there are that measure a convex body's symmetry?

I'll give some context - I have some function on convex bodies and I want to run a computer simulation to find which polytopes with volume 1 and k vertices minimize this functional. It is conjectured that of all bodies of volume 1 a ball will minimize, and I want to gather evidence for or against this conjecture. I'll have to measure symmetry and/or maybe, how close to ellipsoid-like shape a convex polytope is.

Thanks