# Definition:Parallelepiped/Opposite Face

## Definition

The opposite face of the face $F$ of a parallelepiped $P$ is the face of $P$ which is parallel to $F$.

In the above example, the pairs of parallel planes are:

Face $ABCD$ is opposite $HGFE$
Face $ADEH$ is opposite $BCFG$
Face $ABGH$ is opposite $DCFE$

## Also known as

The opposite face can also be referred to as the opposite plane.

## Historical Note

The term opposite face is never actually defined by Euclid, although he refers to the concept throughout:

In the words of Euclid:

If a parallelepidedal solid be cut by a plane through the diagonals of the opposite planes, the solid will be bisected by the plane.