CHIRALITY LIMITS OF CONVEX-BODIES

We use the overlap approach for quantifying the chirality of continuou s figures in order to derive a limit for the chirality coefficient chi (n) of convex sets in n-dimension spaces. The genral definition of chi (n) gives a range of values between 0 and 1. However, it was possible, by making use of the topological properties of convex sets, to reduce the upper bound chi(n) to a lower value: 1-1/2(n-1) (e.g., chi3 = 3/4 in real 3D-space). This upper bound is not the smallest possible one, and could be refined by framing convex bodies by higher-order surface s. Smaller upper bounds of chi(n) can also be found for specific conve x shapes such as polytopes (e.g., tetrahedra in 3D).