Is there a "Most chiral tetrahedron"?

Abstract

A degree of chirality is a function that purports to measure the amount of chirality of an object: it is equal for enantiomers, vanishes only for achiral or degenerate objects and is similarity invariant, dimensionless and normalisable to the interval [0,1]. For a tetrahedron of non-zero three-dimensional volume, achirality is synonymous with the presence of a mirror plane containing one edge and bisecting its opposite, and hence it is easy to design degree-of-chirality functions based on edge length that incorporate all constraints. It is shown that such functions can have largest maxima at widely different points in the tetrahedral shape space, and by incorporation of appropriate factors, the maxima can be pushed to any point in the space. Thus the phrase "most chiral tetrahedron" has no general meaning: any chiral tetrahedron is the most chiral for some legitimate choice of degree of chirality.