Abstract
The \( n \)-dimensional unit hypercubes, \( Q_n \) (\( n=1 \) to \( 4 \)), are used as \( n \)-dimensional graphs (Stereoisograms) to describe the stereoisomeric (enantiomeric and/or diastereomeric) relationships of molecules containing one to four \(
RS \)-stereogenic centers. To achieve this goal, the strings of 0’s and 1’s, used for labelling the vertices of unit hypercubes, are substituted by strings of \( R \)’s and \( S \)’s-descriptors coming from the \( CIP \) priority rules.
The development of those \( n \)-dimensional unit hypercubes along ordered axes and the application of combinatorial techniques allow to locate the enantiomeric pairs at antipodal vertices (points related by a chirality center, which satisfies
the bitwise operation known as "NOT"); whereas diastereomers are related by mirror planes, whose reflection results in a partial permutation of the \( RS \)-descriptors. These facts are in good agreement with the literature and the principles
of the combinatorial theory applied to such hypercubes. On the other hand, because the maximum number of stereoisomers \( 2^n \) is not always held, "pseudo hypercubes" containing one or more "ghost vertices" are proposed to include the
meso (achiral) stereoisomers.
