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We present slight refinements of known general lower and upper bounds onsizes of extended formulations for polytopes. With these observations we areable to compute the extension complexities of all 0/1-polytopes up to dimension4. We provide a complete list of our results including geometric constructionsof minimum size extensions for all considered polytopes. Furthermore, we showthat all of these extensions have strong properties. In particular, one of ourcomputational results is that every 0/1-polytope up to dimension 4 has aminimum size extension that is also a 0/1-polytope.

Computing The Extension Complexities of All 4-Dimensional 0/1-Polytopes