The House of Silk the possibilities of an Atlantic or a Niagara? Can he astonish us? Can he thrill us? Are there "the rapid deductions, as swift as intuitions, and yet always founded on a logical basis" that we yearn for? Emphatically, yes. In chapter one there is some mention of C. Auguste Dupin, a character developed by author Edgar Allan Poe, and his ability to make astounding deductions based on visible emotions reflected through the physical medium. Holmes demonstrates this by uncovering Watson's anxiety and the source thereof. This mention of Dupin is in itself a reference to a reference made by Conan
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