Applying an inversion to this figure gives the Dupin cyclide, and the systole and area of one of these figures is related by Loewner's inequality. The Weyl group can be defined as the normalizer of a group isomorphic to one of these figures, modulo the centralizer of said group. A compact Lie Group has a maximal one of these, and the standard one of these requires seven colors to color according to the Heawood conjecture.
Applying an inversion to this figure gives the Dupin cyclide, and the systole and area of one of these figures is related by Loewner's inequality. The Weyl group can be defined as the normalizer of a group isomorphic to one of these figures, modulo the centralizer of said group. A compact Lie Group has a maximal one of these, and the standard one of these requires seven colors to color according to the Heawood conjecture. Double and triple ones of these have more than one handle, and N-dimensional ones are the direct product of a circle with itself n times. FTP, name this shape important in topology which is homeomorphic to the coffee cup and is shaped like a donut.
Applying an inversion to this figure gives the Dupin cyclide, and the systole and area of one of these figures is related by Loewner's inequality.
Torus