C. Auguste Dupin with artistic imagination. As an observer, he pays special attention to what is unintended, such as hesitation, eagerness or a casual or inadvertent word. Dupin's method also emphasizes the importance of reading and writing: many of his clues come from newspapers or written reports from the Prefect. This device also engages the readers, who follow along by reading the clues themselves. Poe may have gotten the last name "Dupin" from a character in a series of stories first published "Burton's Gentleman's Magazine" in 1828 called "Unpublished passages in the Life of Vidocq, the French Minister of Police". The name also
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