Etymology
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regularity (n.)

"state or character of being regular," c. 1600, from French regularite (14c.), from Medieval Latin *regularitas, from Latin regularis "having rules, containing rules for guidance," from Latin regula "rule, straight piece of wood" (from PIE root *reg- "move in a straight line").

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Definitions of regularity

regularity (n.)
a property of polygons: the property of having equal sides and equal angles;
Synonyms: geometrical regularity
regularity (n.)
the quality of being characterized by a fixed principle or rate;
he was famous for the regularity of his habits
From wordnet.princeton.edu