FEDOROV’S ALGORITHM REVISITED: A COMBINATORIAL APPROACH TO MINERAL POLYHEDRA TAXONOMY. Yu.L. Voitekhovsky, Institute of Geology, Komi Science Centre, Ural Division of RAS, Centre de Geostatistique, Ecole Nationale Superieure des Mines de Paris

A combinatorial approach is used to describe and order the variety of irregular mineral polyhedra that occur in rocks and ores. A face of such a polyhedron is defined to be the intermineral contact surface regardless of its real geometry. Fedorov’s algorithm extended by two cutting operations is used to generate all the 2-, … , 6-hedra (1,393 in common) from the sphere. Lexicographic taxonomy is built for them which may be extended for any n-hedra. The problem of colouring an asymmetric (in generalized sense) n-hedron is solved. The results highlight the great variety of intermineral relations in rocks and ores even in a combinatorial approximation.