This paper introduces Stellar Simplification, a fast implementation of the Four-Face Cluster algorithm. In our version of this mesh simplification scheme, we adopt a probabilistic heuristic that substitutes the priority queue of the original algorithm. This made our version, in average, 40% faster. In our implementation, we adopt a very concise data structure which uses only two arrays of integers to represent the surface topology. We also introduce a new scheme to encode and decode the hierarchy of meshes generated by the simplification algorithm. This scheme can be used for progressive transmission and compression of meshes.