extreme vs vertex

extreme and vertex both are nouns.

Word	Noun	Adjective	Verb	Adverb
extreme	Yes	Yes	No	No
vertex	Yes	No	No	No

As nouns, vertex is a hyponym of extreme; that is, vertex is a word with a more specific, narrower meaning than extreme:

Other hyponyms of extreme include acme, apex, peak.

extreme (noun)	vertex (noun)
the furthest or highest degree of something	the point of intersection of lines or the point opposite the base of a figure
the point located farthest from the middle of something	the highest point (of something)

extreme (adjective)	vertex (adjective)
most distant in any direction
far beyond a norm in quantity or amount or degree; to an utmost degree
of the greatest possible degree or extent or intensity
beyond a norm in views or actions