A new measure of the degree of chirality and asymmetry of a finite num
ber of particles is proposed. To this end a space of configurations of
identical particles is defined as the orbit space of the group of all
permutations of particles embedded in an Euclidean space. This space
is shown to be a metric space and the action of the translation and or
thogonal groups is also defined. The results are applied to the study
of an algebra of polynomials on the configuration space and its equiva
lence to the algebra of symmetric Cartesian tensors is demonstrated. A
n illustrative example is presented. Some general features of chiralit
y are also briefly discussed.