The purpose of this month's article is to bring once more to the public consciousness some work of Sir Roger Penrose, namely "On the Cohomology of Impossible Figures," which appeared in Structural Topology 17 (1961) pp. 11-16 and was reprinted in Leonardo 25, Nos 3/4 (1992) and then as Chapter 4 of The Visual Mind, Michele Emmer, ed., MIT Press, 1993.