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Annex 4 of Representation, Comprehension and Communication of Sets: the Role of Number (1978) Originally published in International Classification, 6, 1979, 2, pp. 92-103
1. In a system with P terms, it should be possible to identify by analysis (with computer assistance and graphic output) configurations of the P terms (linked by Q relationships), selected in order of their degree of symmetry for a given value of P. Constraints on the maximum and minimum value of Q in each case could also be partially determined in terms of symmetry requirements. Tables of such configurations, without considering symmetry, have been produced by Frank Harary ( 124). The less symmetrical structures, for a given P value, should then prove to be those of less probable value in the representation of the central concept -- although possibly of more value in representing an aspect of it. And indeed the "traditional" diagrams are those which are likely to be prominent in the results - although valuable new ones may well be discovered by this procedure.
2. The same procedure may now be applied for the representation of P-term systems in 3 dimensions. Here the symmetry constraints are more severe. This procedure should preferentially select the regular and semi-regular polyhedra (when P is even) or less well-known structures (when P is odd) (22), (23), (125).
3. The procedure may be made more powerful if, for a given P-term system the structure selected is based upon P equal to:
4. A variation on the procedure in 2 dimensions is to allow each term to be represented:
5. Again this variation may be applied in 3 dimensions using simple solids instead of flat shapes. As mentioned earlier the possible configurations are then governed by well-known packing constraints (22), (23).
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