The properties of the root mean square chiral index of a d-dimensional set
of n points, previously investigated for planar sets, are examined for spat
ial sets. The properties of the root mean squares direct symmetry index, de
fined as the normalized minimized sum of the n squared distances between th
e vertices of the d-set and the permuted d-set, are compared to the propert
ies of the chiral index. Some most dissymetric figures are analytically com
puted. They differ from the most chiral figures, but the most dissymetric 3
-tuples and the most chiral 3-tuples have a common remarkable geometric pro
perty: the squared lengths of the sides are each equal to three times a squ
ared distance vertex to the mean point. (C) 1999 American Institute of Phys
ics. [S0022-2488(99)01009-9].