Seashells: the plainness and beauty of their mathematical description

Examples: Gastropods

Worm shell (West Indian worm shell, variable shape, [2, p. 49])

[alpha=83, beta=8, phi=55, mu=10, Omega=2, A=180, a=16, b=16, L=0]

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All worm shells, or vermetidae, as their name suggests, are irregularly coiled and resemble worm tubes. They are unusual shells which look like long tubes, evenly spirally coiled at the apex and then loosely and irregularly so. They first grow like typical snails (in their earlier growth stages, some are almost indistinguishable from turritella and their anatomy shows they are related) but then cement themselves to a hard substrate and begin twisting and meandering unpredictably (generally coil upon themselves). The worm shell of West Indies, although grouped with other worm shells, is actually a screw shell which has unwound itself, a point proved if you examine the animal that formed it.
Habitat: sand or in sponges, West Indies.

[2] S. Peter Dance, Shells, Dorling Kindersley, 2002.

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