What is a description of the symmetry of sphere?

Answer 1

Group theory is of particular significance to the study of objects having plenty of symmetry. The sphere is a good example; its self-equivalences include arbitrary rotations in three dimensions about the centre.

Notice that for any two points on the sphere, there is a self-equivalence (i.e., rotation) taking one of the points to the other.

The sphere is homogeneous, a technical word meaning "having lots of symmetry"! A special role is played by the set of self-equivalences fixing a single point (in this case, the rotations about a fixed axis); it is called the isotropy subgroup of the symmetry.

Answer 2

A figure that has infinite equidistant points in three dimensions from a specified center.