Seashells: the plainness and beauty of their mathematical description

Examples: Gastropods: adding ridges

The Precious Wentletrap (corkscrew shape, [2, p. 53])

[alpha=86, beta=10, phi=-45, mu=5, Omega=1, A=90, a=20, b=20, L=14, W1=180, W2=.4, P=40, N=180]

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The Precious Wentletrap or Staircase Shell (Epitonium scalare), of the family Epitoniidae, is so exquisitely formed that it is no wonder the early collectors in the 18th Century valued it above rubies and paid prices for which it might have been copied in gold and studded with diamonds. The popular name for these delicate and attractive shells comes from the Dutch word for a winding staircase. The tapering spiral whorls of this small, dainty shell which reaches not much more than two inches in length, are not sutured together as in the case with most spiral univalves. There is a space between them all the way from the nucleus to the aperture and the whole is covered with very regular and ridge-like varices which have the appearance of a white latticework cage enclosing the glossy whorls, or the treads of a spiral staircase. Though no longer considered rare (it has become much more common during the last four decades), they are still greatly admired and fine specimens as much coveted as ever, but their prices nowadays are a modest fraction of earlier times.
Habitat: subtidal in sand, Indo-Pacific.

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

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