In this paper we focus on an unsupervised classification case, where clusters share a common "shape". We consider that this shape consists of a given hyperplane, common to all clusters up to a given a translation. Points are thus considered as distributed around a set of parallel hyperplanes. The underlying objective function can be seen as minimizing the sum of distances of each point to its hyperplane. Similarly to k-means, this goal is achieved by alternating affectation- (of each point to an hyperplane) and computation- (of the hyperplane equation) phases. Seeking for parallel hyperplanes, this computation phase is conducted simultaneously for all hyperplanes.