In mathematics, existence is logical possibility. To say "There exists a polygon with 7 sides" is to say that a plane figure's having 7 sides does not logically exclude its being a polygon. Since all mathematical "objects" are ideal, "existence" is not construed to mean physical existence.
While "existence" means possibility or non-self-contradiction,"constructibility" refers to describing a specific object of said type. For example "The plane figure with 7 sides all of equal length whose adjacent sides all meet at an angle of 5π/7 radians" describes a specific 7-gon.
This mathematics-related article is a stub. You can help Wikipedia by expanding it.