This paper presents the R package PPCI which implements three recently proposed projection pursuit methods for clustering. The methods are unified by the approach of defining an optimal hyperplane to separate clusters, and deriving a projection index whose optimiser is the vector normal to this separating hyperplane. Divisive hierarchical clustering algorithms that can detect clusters defined in different subspaces are readily obtained by recursively bi-partitioning the data through such hyperplanes. Projecting onto the vector normal to the optimal hyperplane enables visualisations of the data that can be used to validate the partition at each level of the cluster hierarchy. PPCI also provides a simplified framework in which the clustering models can be modified in an interactive manner. Extensions to problems involving clusters which are not linearly separable, and to the problem of finding maximum hard margin hyperplanes for clustering are also discussed.