The noun vertex has two meanings: (1) the highest point, and (2) the point at which the sides of an angle intersect. Vortex refers to a whirling mass of matter. Both are often used metaphorically—vertex for the meeting point between two or more things, and vortex for any chaotic, figuratively swirling mass.
Though the words have no definitions in common, they’re both derived from the Latin vertere, meaning to turn. Each is pluralized in a pair of ways—vertexes/vertices, and vortexes/vortices. Each word’s -ices version is more common than the -exes version, but neither form is more correct than the other.
Examples
The point where the arcs intersect marks the third vertex of your equilateral triangle. [Science Magazine]
A boat was caught in the vortex of a whirlpool at sea. [Winnipeg Free Press]
Imagine a triangle with Student, Teacher, and Subject at the vertices. [The Times Record]
Rather, it repeatedly flings its wings forward to create tiny vortices of pressurized air. [Popular Science]
As it happens, Ms. Romero’s downtown Los Angeles office where we meet is located at the vertex of what she calls “the Bermuda Triangle.” [Daily Markets]
We are subject to vortexes of nothingness, chaos and death. [Pasadena Sun]