The Murders in the Rue Morgue as the first detective fiction story, the character of Dupin became the prototype for many future fictional detectives, including Arthur Conan Doyle's Sherlock Holmes and Agatha Christie's Hercule Poirot. The genre is distinctive from a general mystery story in that the focus is on analysis. Poe's role in the creation of the detective story is reflected in the Edgar Awards, given annually by the Mystery Writers of America. "The Murders in the Rue Morgue" also established many tropes that would become common elements in mystery fiction: the eccentric but brilliant detective, the bumbling constabulary, the first-person narration by a close
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