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Definition: Def. 11.13: Prism, Parallelepiped

(Definition 13 from Book 11 of Euclid's “Elements”)

A prism is a solid figure, contained by planes, of which the two opposite (planes) are equal, similar, and parallel, and the remaining (planes are) parallelograms.

Modern (Generalized) Formulation

A prism (or a hexahedron, or a parallelepiped) is a three-dimensional polyhedron with two congruent opposite convex rectilinear figures and the remaining faces being parallelograms. Important special cases of prisms are:

• parallelepiped - a prism, whose two congruent faces are also parallelograms,
• rectangular parallelepiped - a parallelepiped, whose opposite faces are rectangles or squares.

Examples

Some general prisms, whose opposite congruent convex faces are triangles (left) or trapezia (right):

A paralellelepiped (left) and a rectangular parallelepiped (right):

Mentioned in:

Corollaries: 1 2
Definitions: 3
Lemmas: 4
Proofs: 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Propositions: 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

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References

Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

1. Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016