Seashells: the plainness and beauty of their mathematical description

Examples: Gastropods

Tiger Maurea (top shape, [2, p. 35])

[alpha=84.9, beta=7, phi=-36, mu=1, Omega=-2, A=47, a=40, b=19, L=0]

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adding ridges

Commercial Trochus (top shape, [2, p. 38])

[alpha=87, beta=15, phi=-45, mu=5, Omega=1, A=95, a=20, b=20, L=20, W[1]=.5, W[2]=3, P=10, N=8]

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The top shape shells belong to the family of Trochidae, that includes hundreds of species distributed worldwide. The tiger maurea is a thin but strongly built shell with a large body whorl and steeply sloping spire, ending with a sharply pointed apex. Pigments often are present only on the exterior and do not permeate the entire shell fabric.
Habitat: Intertidal rocks, New Zealand.
The commercial trochus, the largest and heaviest of the top shells, is almost an equilateral triangle in profile. Once used to provide the material for buttons, this is the reason for its name.
Habitat: very common is the tropical Indo-Pacific region, near coral reefs.

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

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