vertex vs point of intersection

vertex and point of intersection both are nouns.

Word	Noun	Adjective	Verb	Adverb
vertex	Yes	No	No	No
point of intersection	Yes	No	No	No

As nouns, point of intersection is a hypernym of vertex; that is, point of intersection is a word with a broader meaning than vertex:

vertex: the point of intersection of lines or the point opposite the base of a figure
point of intersection: a point where lines intersect

Other hypernyms of vertex include intersection, intersection point.

vertex (noun)	point of intersection (noun)
the point of intersection of lines or the point opposite the base of a figure	a point where lines intersect
the highest point (of something)