Nucleophilic displacement on phosphorus in cyclic phosphonium salts by external nucleophiles is believed to proceed through intermediate phosphoranes, and similar intermediates are involved in internal nucleophilic displacements at phosphorus in acyclic phosphonium salts. The stereochemical consequences (retention or inversion) of such substitution reactions may be systematically and conveniently discussed with the aid of a modification of Balaban's 20-vertex graph, which has the appearance of the carbon skeleton of hexaasterane. Eighteen vertices represent the eighteen stereoisomers of intermediate phosphoranes containing five different ligands, two of which are termini of a ring system incapable of spanning the two apical positions. Twenty-four edges represent the alternative pathways for interconversion of the isomers by pseudorotation. In an idealized (D6h) representation, three planes intersect at the sixfold axis. Each plane divides the graph into two subsets of nine vertices. Each subset represents the nine phosphoranes resulting from external nucleophilic attack on the phosphorus atom of a given enantiomer of a cyclic phosphonium salt. The stereochemical outcome of the displacement is thus given by the positions of intermediate phosphoranes within sectors defined by two intersecting planes. Two additional, scalloped surfaces, whose threefold axis is coincident on the sixfold axis of the idealized figure, divide the graph into two subsets of nine vertices. Each subset contains all the phosphoranes which result from internal nucleophilic attack on the phosphorus atom of a given enantiomer of an acyclic phosphonium salt. A novel topological overview is thus provided of the multiplicity of accessible pathways in such displacement reactions, and of the stereochemistry of these displacements. The scheme is a general one, and is readily extended to any displacement reaction on a tetracoordinate atom which involves the intermediacy of a trigonal-bipyramidal pentacoordinate species of moderate lifetime. The application of such extensions to cognate systems is indicated. © 1969, American Chemical Society. All rights reserved.