C. Auguste Dupin Vanished Treasure" (May 1965) and "The Fires in the Rue St. Honoré" (January 1967). This collection was subsequently published in England by Tom Stacey in 1972 as "Murder in the Rue Royale and Further Exploits of the Chevalier Dupin" and included a further five stories written since the original publication. Dupin had considerable impact on the Agatha Christie character Hercule Poirot, first introduced in "The Mysterious Affair at Styles" (1920). Later in the fictional detective's life, he writes a book on Edgar Allan Poe in the novel "Third Girl" (1966). "The Man Who Was Poe", a juvenile novel by Avi,
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