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WordNet records no synonym and no antonym for equator. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
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.
an imaginary line around the Earth forming the great circle that is equidistant from the north and south poles
“the equator is the boundary between the northern and southern hemispheres”
a circle dividing a sphere or other surface into two usually equal and symmetrical parts
Synonyms, antonyms and the broader and narrower relations for equator come from Princeton University’s WordNet. Full sources and licences.