Sherlock Holmes such that many have believed him to be not a fictional character but a real individual; numerous literary and fan societies have been founded that pretend to operate on this principle. Widely considered a British cultural icon, the character and stories have had a profound and lasting effect on mystery writing and popular culture as a whole, with the original tales as well as thousands written by authors other than Conan Doyle being adapted into stage and radio plays, television, films, video games, and other media for over one hundred years. Edgar Allan Poe's C. Auguste Dupin is generally acknowledged
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