Definition:Tetrahedron/Apex
Definition
Once the base of a tetrahedron has been identified, the vertex which does not lie on the base is called the apex of the tetrahedron.
In the above diagram, given that the base of the tetrahedron $ABCD$ is the triangle $ABC$, the apex is $D$.
As all faces of a tetrahedron are triangular by definition, it follows that each of its vertices is the common point of three triangles.
Therefore is qualitatively immaterial which vertex is determined to be the apex.
This definition is compatible with the definition of the apex of a general pyramid.
Also known as
The apex of a tetrahedron is seen in some sources (for example Euclid's The Elements) as vertex.
However, the term vertex can be used to define any of the corners of a polyhedron, so its use in this context is limited.
Also see
Linguistic Note
The plural of apex is apices, which is pronounced ay-pi-seez.
The form apexes can often be seen, but this is technically incorrect.
Compare vertex, whose plural is vertices.
Hence the colloquial phrase base over apex as the description of a particularly flamboyant physical tumble.