The Poe Shadow October 8, 1849. He had previously corresponded with Poe about providing legal support for a new publication, "The Stylus". Clark feels obliged to look into the mysterious circumstances surrounding Poe's death, despite protests from his fiancée Hattie Blum and his friend Peter Stuart. Clark's journey takes him to Paris to seek out the real-life inspiration for Poe's character C. Auguste Dupin, a man of intellect who could help unravel the mystery. After eliminating several possibilities, he meets Baron C.A. Dupin, a famous lawyer, and a detective with a similar name, Auguste Duponte. After a confrontation with the Baron Dupin and
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