Arthur Conan Doyle study of such a character [viz., Bell] I used and amplified his methods when in later life I tried to build up a scientific detective who solved cases on his own merits and not through the folly of the criminal." Robert Louis Stevenson was able, even in faraway Samoa, to recognise the strong similarity between Joseph Bell and Sherlock Holmes: "My compliments on your very ingenious and very interesting adventures of Sherlock Holmes. ... can this be my old friend Joe Bell?" Other authors sometimes suggest additional influences—for instance, the famous Edgar Allan Poe character C. Auguste Dupin. Dr. (John)
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