The Murders in the Rue Morgue Poe's Dupin displays many traits which became literary conventions in subsequent fictional detectives, including Sherlock Holmes and Hercule Poirot. Many later characters, for example, follow Poe's model of the brilliant detective, his personal friend who serves as narrator, and the final revelation being presented before the reasoning that leads up to it. Dupin himself reappears in "The Mystery of Marie Rogêt" and "The Purloined Letter". The unnamed narrator of the story opens with a lengthy commentary on the nature and practice of analytical reasoning, then describes the circumstances under which he first met Dupin during an extended visit to Paris.
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