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 $13$)
Parts of Prism
Base
The bases of a prism are the two parallel polygons which form the faces at either end of the prism.
Lateral Face
The lateral faces of a prism are the parallelogramic faces which join the bases.
Lateral Edge
The lateral edges of a prism are the edges which join the vertices of the lateral faces.
In the above diagram, the edges $AF, BG, CH, DI$ and $EJ$ are the lateral edges 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 $P_2$.
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 $AJ$.
Nomenclature
The polygon which is the base of a prism $P$ determines the name of the type of $P$.
Triangular
A triangular prism is a prism whose bases are triangles.
Quadrangular
A quadrangular prism is a prism whose bases are quadrilaterals.
Pentagonal
A pentagonal prism is a prism whose bases are pentagons.
Hexagonal
A hexagonal prism is a prism whose bases are hexagons.
Also defined as
Some sources insist that the bases of a prism need to be convex.
Also see
- Results about prisms can be found here.
Linguistic Note
The adjectival form of prism is prismatic.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): prism
- 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
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): prism