There are of course 3 regular tilings of the plane by copies of one regular polygon. There are 8 more if several regular polygons are used, with the regularity condition being that the group of tile-preserving isometries of the plane is transitive on the set of all vertices: the tiling is "vertex-regular". (9 more if you distinguish between mirror images, but it's more natural not to.) * * * The natural generalization to 3-space would ask for all vertex-regular tilings of space by: a) any collection of regular polyhedra OR, what is perhaps more interesting, b) any collection of regular and/or Archimedean polyhedra. (There are 13 Archimedean polyhedra if we don't distinguish between mirror images.) Has anyone seen a classification of either case a), or better, case b) ??? --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele