See also: Mathematics of Seashells.
The biological classification hierarchy: “Kindom:Phylum:Class:Order:Family:Genus:Species”.
The shells animals are of Kindom Animalia (that is, animals), and Phylum Mollusca (they are mollusks). Mollusks have two major class: Gastropoda (gastropods) and Bivalvia (bivalves). Gastropods are those with spiral shells. Snails slugs limpets and abalone are all gastropods. Bivalves are those clam-like shells, including mussell, cockle, clam, oyster.
〔National Audubon Society Field Guide to North American Seashells by Harald A Rehder. Buy at amazon〕