# Definition:Prism

## Definition

In the words of Euclid:

*A***prism**is a solid figure contained by planes of which, namely those which are opposite, are equal, similar and parallel, while the rest are parallelograms.

(*The Elements*: Book $\text{XI}$: Definition $13$)

## Faces of Prism

### Base

The **bases** of a prism are the two parallel polygons which form the faces at either end of the prism.

In the above diagram, the faces $ABCDE$ and $FGHIJ$ are the **bases** of the prism.

### Lateral Face

The **lateral faces** of a prism are the parallelogramic faces which join the bases.

In the above diagram, the faces $ABGF, BCHG, CDIH, DEJI$ and $EAFJ$ are the **lateral faces** of the prism.

### Opposite

Let $P$ be a prism whose bases are $P_1$ and $P_2$.

The **opposite face** of the base $P_1$ is the base $P_2$.

In the above example, the base $ABCDE$ is opposite $FGHIJ$.

## Height

The **height** of a prism is the length of the perpendicular between the bases of the prism.

In the above diagram, the distance $h$ is the **height** of the prism $AJ$.

## Sources

- 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**prism**