Definition:Parallelepiped/Opposite Face

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Definition

Parallelepiped.png

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.

(The Elements: Book $\text{XI}$: Proposition $28$)