sphere has 13 distinct synonyms spread across 4 of its 7 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
the geographical area in which one nation is very influential
a particular aspect of life or activity
“he was helpless in an important sector of his life”
a solid figure bounded by a spherical surface (including the space it encloses)
a three-dimensional closed surface such that every point on the surface is equidistant from the center
the apparent surface of the imaginary sphere on which celestial bodies appear to be projected
Synonyms, antonyms and the broader and narrower relations for sphere come from Princeton University’s WordNet. Full sources and licences.