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In mathematics, a Dupin cyclide or cyclide of Dupin is any geometric inversion of a standard torus, cylinder or double cone. In particular, these latter
sphere geometry is the transformation by reciprocal directions or Laguerre inversion, being a generator of the Laguerre group. It transforms not only spheres
components are always closed. It is a subgroup since multiplication and inversion in a topological or algebraic group are continuous maps by definition