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Consider a cone consisting of the set of all straight lines joining the boundary of a plane figure $PQR$ to a point $A$ not in the same plane of $PQR$:


In the above diagram, the point $A$ is known as the apex of the cone.

Also known as

The apex of a cone is also known as its 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.

Hence the colloquial phrase base over apex as the description of a particularly flamboyant physical tumble.