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WordNet records no synonym and no antonym for isometry. 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.
the growth rates in different parts of a growing organism are the same
a one-to-one mapping of one metric space into another metric space that preserves the distances between each pair of points
“the isometries of the cube”
Synonyms, antonyms and the broader and narrower relations for isometry come from Princeton University’s WordNet. Full sources and licences.
equality of elevation above sea level
equality of measure (e.g., equality of height above sea level or equality of loudness etc.)