Definition:Prism/Base
Definition
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.
Lower Base
One of the two bases of a prism is distinguished from the other one, and identified as the lower base.
The prism is then situated so that its lower base appears at the bottom of its depiction in whatever diagram it is used in.
In the above diagram, the face $ABCDE$ would be identified as being the lower base of the prism.
Upper Base
Once the lower base of a prism has been identified, the remaining face can then be referred to as the upper base.
The upper base will then be situated at the top of its depiction in a diagram.
In the above diagram, the face $FGHIJ$ would be identified as being the upper base of the prism.
Also known as
The bases of a prism can be referred to as their end faces or endfaces.
The term base can suggest that the prism be specifically situated so that one of the end faces is coincident with a plane of reference, which may be misleading.
Also defined as
Although the base of a prism is generally understood to be one of the opposite faces which defines the prism, Euclid was inconsistent in his usage in The Elements.
In his Proposition $39$ of Book $\text{XI} $: Prisms of equal Height with Parallelogram and Triangle as Base, he defines the base of one prism as being one of the opposite parallel faces, but of the other he defines the base as being an arbitrary one of the parallelograms.
Using this definition, the parallelogram $PQTS$ in the above diagram is the base of the prism $PQRSTU$.
Also see
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): prism
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): prism