Representation of stereochemistry using combinatorial maps

Abstract

N-dimensional maps are combinatorial models defined for representing the topology of subdivisions of n-dimensional geometric spaces, i.e., the topology of partitions of the spaces into i-dimensional cells (vertices, edges, faces, volumes, etc.; 0≤i≤n) [P. Lienhardt, Internat. J. Comput. Geom. Appl. 4 (1994), no. 3, 275–324; MR1296150 (95h:52029)]. They provide the basis for a simple, uniform, and general computer representation of the relative spatial arrangement of atoms in stereogenic entities. This article illustrates the use of 2-dimensional maps as a non-geometric computer representation of convex polyhedral and polygonal stereogenic entities, thus covering the vast majority of stereochemical atomic configurations, bond conformations, etc.