Hyperrectangle

A rectangular cuboid is a 3-orthotope

In geometry, an orthotope^[1] (also called a hyperrectangle or a box) is the generalization of a rectangle for higher dimensions, formally defined as the Cartesian product of intervals.

A three-dimensional orthotope is also called a right rectangular prism, rectangular cuboid, or rectangular parallelepiped.

A special case of an n-orthotope, where all edges are equal length, is the n-hypercube.^[1]

By analogy, the term "hyperrectangle" or "box" refers to Cartesian products of orthogonal intervals of other kinds, such as ranges of keys in database theory or ranges of integers, rather than real numbers.^{[citation needed]}

See also

• Bounding box

Notes

1. ^ ^{a b} Coxeter, 1973

References

• Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, pp. 122-123, 1973.

External links

• Weisstein, Eric W., "Rectangular parallelepiped" from MathWorld.
• Weisstein, Eric W., "Orthotope" from MathWorld.

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