Apex and vertex are so often used interchangeably with reference to the tip or top point of a cone, a pyramid, or a conic section that a fundamental difference in implications is often ignored.
Apex has particular reference to the sharpness or angularity of the point or tip; it may or may not in its literal application to things imply that this is the highest point.
- the apex of the heart is its lower and pointed end
- the apex of a lung is its upper coneshaped end
Apex may also refer to the converging point of two lines whether they extend in a vertical plane or not.
- apex of a leaf
- apex of a vein in a mine
Vertex as a rule, and apart from some technical senses in mathematics, implies a base (real or assumed) and therefore a top or highest point.
This implication is retained when the word is applied to concrete things; thus, the vertex of the head or of the skull is the highest point or the upper end of its axis; vertex in astronomy is the zenith either with reference to the observer or to the particular body under observation.