# 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**.

## 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.