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 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