Plural of angularity; multiple instances of having angles, corners, or being angular in form; the quality of being sharp or pointed.
From 'angular' plus '-ity' (quality of), then pluralized with '-ies.' The suffix '-ity' transforms adjectives into nouns representing abstract qualities.
The jump from 'angular' to 'angularities' shows English's love of abstraction—we go from 'having angles' (adjective) to 'the quality of having angles' (abstract noun) to 'multiple instances of that quality' (plural)!
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