From a computer analysis of the spatial organization of the secondary structures of beta-sandwich proteins, we find certain sets of consecutive strands that are connected by hydrogen bonds, which we call "strandons." The analysis of the arrangements of strandons in 491 protein structures that come from 69 different superfamilies reveals strict regularities in the arrangements of strandons and the formation of what we call "canonical supermotifs." Six such supermotifs account for approximately 90% of all observed structures. Simple geometric rules are described that dictate the formation of these supermotifs.