C. Auguste Dupin Montfaucon" by (2004), a collection of thirteen detective stories set in the 19th century, the last of which (« Le drame de Reichenbach ») also provides a link with Sherlock Holmes. Other appearances: Jorge Luis Borges pays homage to Poe's Dupin in "Death and the Compass", by calling his main detective character Erik Lönrott an "Auguste Dupin"-type detective. This is one of the stories published by Borges in his "Ficciones"(1944). Borges also translated Poe's works into Spanish. In "The Paralogs of Phileas Fogg", author James Downard has Dupin help Fogg and his cohorts resolve some issues during the American leg
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