PUZZLE: There is a closed metric surface S that can be tiled by N regular polygons for all but two values of N in the range 1 <= N <= 10. Find a surface S satisfying this condition and prove that it works. ____________________________________________________________ Notes: Closed means of finite extent and without boundary. A tiling means S is the union of regular polygons such that if P and Q are distinct polygons, then their intersection is either empty or a union of common vertices and/or edges. Also, some of one polygon's own edges may coincide pairwise. A regular polygon Q of k sides inherits its metric from S such that the isometry group of Q has 2k elements. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele