Search for internal diagonals in polyhedration of reciprocal systems by the algorithm for topological correction of lists of simplexes of different dimensions

The algorithm for topological correction of lists of simplexes of different dimensions was used for analyzing the published methods for determining internal diagonals in polyhedration of reciprocal systems. By this algorithm, errors were found in the polyhedration of the quaternary systems Ca,Na,KaEuro-F,MoO4, K,Na,LiaEuro-Cl,NO3, Ba,Na,KaEuro-F,MoO4, Na,KaEuro-Cl,NO3,NO2, and Li,K,BaaEuro-F,WO4 and the quinary system Li,K,Ca,BaaEuro-F,WO4, which were used for illustrating the application of the methods. Advantages of the algorithms were demonstrated in cases of competition of internal secants.