Edgar Allan Poe 19th century to become more popular in Europe than in the United States. Poe is particularly respected in France, in part due to early translations by Charles Baudelaire. Baudelaire's translations became definitive renditions of Poe's work throughout Europe. Poe's early detective fiction tales featuring C. Auguste Dupin laid the groundwork for future detectives in literature. Sir Arthur Conan Doyle said, "Each [of Poe's detective stories] is a root from which a whole literature has developed... Where was the detective story until Poe breathed the breath of life into it?" The Mystery Writers of America have named their awards for excellence
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