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 that the class of Dupin cyclides is invariant under Möbius (or conformal) transformations. In complex space formula_2 these three latter varieties can be mapped to one another by inversion, so Dupin cyclides can be defined as inversions of the torus (or the cylinder, or the double cone). Since a standard torus is the orbit of a point under a two dimensional abelian subgroup of the Möbius group, it follows that the cyclides also are, and this provides a second way to define them. A third property which characterizes Dupin cyclides is that their curvature lines are all circles (possibly through