Mandalas for Diagrammatical Representation of Stereoisomerism

Abstract

A new concept "mandala" is proposed in order to comprehend the relationship between molecular symmetry and combinatorics. A regular body of a given symmetry (G) is defined by a three-dimensional skeleton having the same number of symmetry-equivalent vertices as the order of the group G. A mandala is defined as a nested regular body in which each vertex is occupied by a regular body. The regular body represents an intramolecular symmetry, while the mandala represents an intermolecular symmetry (stereoisomerism). Thereby, combinatorial enumeration of stereoisomers can be formulated rationally.