Crime fiction by the Danish author Steen Steensen Blicher, published in 1829. Better known are the earlier dark works of Edgar Allan Poe. His brilliant and eccentric detective C. Auguste Dupin, a forerunner to Arthur Conan Doyle’s Sherlock Holmes, appeared in works such as "The Murders in the Rue Morgue" (1841), "The Mystery of Marie Roget" (1842), and "The Purloined Letter" (1844). With his Dupin stories, Poe provided the framework for the classic detective story. The detective’s unnamed companion is the narrator of the stories and a prototype for the character of Dr. Watson in later Sherlock Holmes stories. Wilkie Collins' epistolary
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