Is there a way to quantify the chirality of a 3d shape?

A propeller is a chiral structure. Propellers can have low or large pitch. This difference can be seen as distinguishing propellers of low and of large chirality.

Is there a general way, given a closed 3d shape, to quantify its chirality? Is there some sort of integral over the shape that yields a number quantifying the degree of chirality of that shape?

• The Hausdorff distance to its mirror image? Or rather, the inf of the distances to the confgruent copies of its mirror image, I guess. Oct 28, 2022 at 19:50
• In a word yes, though presumably the underlying intent is a measure satisfying additional conditions: 1. real-valued, 2. easily-calculated, 3. widely-used. Offhand I don't know of anything satisfying both 1. and 2., and nothing satisfying 3. Oct 28, 2022 at 19:51
• Where can I read more about the Hausdorff distance? Oct 29, 2022 at 14:53
• Complex-valued is also ok ... Oct 29, 2022 at 14:54
• For posterity: re-asked here mathoverflow.net/questions/433487/… Oct 30, 2022 at 17:03