symmetric vs symmetry

symmetric is not a noun while symmetry is a noun.

Word	Noun	Adjective	Verb	Adverb
symmetric	No	Yes	No	No
symmetry	Yes	No	No	No

symmetric (noun)	symmetry (noun)
	(mathematics) an attribute of a shape or relation; exact reflection of form on opposite sides of a dividing line or plane
	(physics) the property of being isotropic; having the same value when measured in different directions
	balance among the parts of something

symmetric (adjective)	symmetry (adjective)
having similarity in size, shape, and relative position of corresponding parts