irregularity vs asymmetry

irregularity and asymmetry both are nouns.

Word	Noun	Adjective	Verb	Adverb
irregularity	Yes	No	No	No
asymmetry	Yes	No	No	No

As nouns, asymmetry is a hypernym of irregularity; that is, asymmetry is a word with a broader meaning than irregularity:

irregularity (noun)	asymmetry (noun)
behavior that breaches the rule or etiquette or custom or morality	(mathematics) a lack of symmetry
not characterized by a fixed principle or rate; at irregular intervals
an irregular asymmetry in shape; an irregular spatial pattern
irregular and infrequent or difficult evacuation of the bowels; can be a symptom of intestinal obstruction or diverticulitis