A dimensional analysis shows that all chiral labeled and unlabeled sim
plexes in E(2), and all maximally labeled simplexes in higher dimensio
ns, are unique in that they can be partitioned into disjoint heterochi
ral sets. Such partition is impossible for all other labeled and unlab
eled m-point sets (m greater than or equal to n + 2) in E(n), since th
ey and their enantiomorphs are chirally connected.