ABSTRACT
A set of open (closed) circles is said to form a packing (covering) on the sphere, or in the Euclidean or hyperbolic plane if every point of the sphere or plane belongs to at most (at least) one circle of the set. Following a concept introduced by L.Fejes Tóth [4] we say that a packing (covering) is solid if no finite number of its members can be rearranged so as to form, together with the rest of the members, a packing (covering) not congruent to the original one. A solid packing of equal circles in the Euclidean plane is always a densest packing of equal circles, and similarly for coverings. A solid packing of n equal circles on the sphere is always a densest packing of n equal circles, and similarly for coverings. Note, however, that the converse is not true.
