Prism (geometry)
In geometry, a prism is a polyhedron made of two parallel copies of some polygonal base joined by faces that are rectangles or parallelograms. All parallel cross-sections along its length are also the same. A prism is a special case of a prismatoid.
A right prism is a prism in which the joining edges and faces are perpendicular to the base faces. This applies iff the joining faces are rectangular.
Prisms can be triangular, quadrilateral, rectangular, square, pentagonal (also known in optics as a pentaprism), hexagonal, etc., according to the shape of the base faces. For each we can distinguish general and right versions.
A parallelepiped is a prism of which the base is a parallelogram, or equivalently a polyhedron with 6 faces which are all parallelograms.
In the case of a rectangular or square prism there may be ambiguity because some texts may mean a right rectangular prism and a right square prism.
A right rectangular prism is also called a cuboid, or informally a rectangular box. A right square prism is simply a square box, and may also be called a square cuboid.
A regular right prism is a right prism with all edges of equal length. All faces are regular polygons: two n sided ones, and n squares. For n=4 all are squares and we have the cube, which is also edge- and face-uniform and so is a Platonic solid. In some texts "regular" may imply "right", but anyway the term has a weaker meaning than in the sense of "regular polyhedron", because the only prism which is regular in that strong sense is the cube.
Right prisms with regular bases form one of the two infinite series of vertex-uniform polyhedra, the other series being the antiprisms. The dual of a prism is a bipyramid.
The volume of a prism is the product of the area of the base and the distance between the two base faces (in the case of a non-right prism, note that this means the perpendicular distance).
External links
- Paper models of prisms and antiprisms
- Prisms (Cross Section Illustration)
- The Uniform Polyhedra
- Virtual Reality Polyhedra The Encyclopedia of Polyhedra