  Chirality, the lack of inversion symmetry, is a geometrical property critical
to chemistry, biology and material sciences. In the three-dimensional Euclidean
space $\mathbb{R}^3$ chriality can ususally be characterized with four-point
structrual information. Various functions have therefore been proposed to
quantify chirality of tetrahedra, which can be extended to other 3D objects,
including molecules. However, existing functions are scalars or pseudoscalars
and are unable to simultaneously possess all the desirable properties of
chirality functions: detectability of chirality, inversion antisymmetry and
continuity. We observe that to avoid this difficulty, any chirality function
for tetrahedra must be a pseudovector with at least two components. In light of
this, we propose a two-component pseudovectoral chirality function for
tetrahedra that satisfies all the desirable properties. We plan to use this
function to map the "chiral zeros" of existing pseudoscalar chirality functions
and to design a microstructure descriptor for the chirality of many-body
systems and multi-phase media in $\mathbb{R}^3$.
