C. Auguste Dupin Dostoevsky called Poe "an enormously talented writer" and favorably reviewed Poe's detective stories. The character Porfiry Petrovich in Dostoevsky's novel "Crime and Punishment" was influenced by Dupin. In the first Sherlock Holmes story, "A Study in Scarlet" (1887), Doctor Watson compares Holmes to Dupin, to which Holmes replies: "No doubt you think you are complimenting me ... In my opinion, Dupin was a very inferior fellow... He had some analytical genius, no doubt; but he was by no means such a phenomenon as Poe appears to imagine". Alluding to an episode in "The Murders in the Rue Morgue", where Dupin
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