Description of the topological formulation of finger-print patterns is given and illustrated by examples. In particular, the way of setting up a dictionary of total finger pattern types for the two hands separately and combined is explained. Samples of 302 normal individuals, 225 complete 21-trisomics and 173 incomplete 21-trisomics are analysed here using this method. The frequencies of the commonest total finger pattern types are compared in the three groups, using dictionaries, in which all the formulae have been listed. The mean values of radial and ulnar components for each pair of homologous fingers separately are also compared. The method is recommended for comparisons of populations, particularly if the use of a computer is expected; it can also be helpful in evaluating the total finger pattern type of any individual, in terms of the probability of belonging to one population or another, particularly if the total palmar and sole pattern types can be compared as well. Some limitations of the method from a statistical point of view are also discussed.