# 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.

## 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.