Gentleman detective shares some features with the later gentleman detective. He was "…the first fictional detective of importance and the model for virtually every cerebral crime solver who followed." More specifically, Dorothy L. Sayers noted that "Sherlock Holmes modelled himself to a large extent upon (Poe's) Dupin, substituting cocaine for candlelight, with accompaniments of shag and fiddle-playing." Dupin is French, not English, but is probably a "gentleman". He comes from a once wealthy family but has been reduced "by a variety of untoward events" to more humble circumstances. He is entirely amateur and contents himself only with the basic necessities of life.
Dupin cyclide of Dupin cyclides is invariant under the larger group of all Lie sphere transformations; any two Dupin cyclides are Lie-equivalent. They form (in some sense) the simplest class of Lie-invariant surfaces after the spheres, and are therefore particularly significant in Lie sphere geometry. The definition also means that a Dupin cyclide is the envelope of the one-parameter family of spheres tangent to three given mutually tangent spheres. It follows that it is tangent to infinitely many Soddy's hexlet configurations of spheres. A further special property of a cyclide is: An elliptic cyclide can be represented parametrically by the following formulas