The apex of a geometric figure is the point which is distinguished from the others by dint of it being furthest away from its base.
Not all figures have a discernible apex; for example, parallelograms, prisms and parallelepipeds do not.
Apex of Triangle
Having selected one side of a triangle to be the base, the opposite vertex to that base is called the apex.
In the above diagram, if $AC$ is taken to be the base of $\triangle ABC$, then $B$ is the apex.
Apex of Isosceles Triangle
The vertex opposite the base of an isosceles triangle is called the apex of the triangle.
In the above diagram, $A$ is the apex.
Apex of Cone
In the above diagram, the point $A$ is known as the apex of the cone.
Apex of Pyramid
The vertex of a pyramid which is the common vertex of its triangular faces is called the apex of the pyramid.
In the above diagram, $Q$ is the apex.
The plural of apex is apices, which is pronounced ay-pi-seez.
The form apexes can often be seen, but this is technically incorrect.
Hence the colloquial phrase base over apex as the description of a particularly flamboyant physical tumble.
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): apex
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): apex (plural apices)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): apex (plural apices)
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): apex (apices)