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In geometry, an n-orthotope (also called a hyperrectangle or a box) is the generalization of a rectangle for higher dimensions, formally defined as the Cartesian product of intervals.
Contents
Types
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-cube.
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.
Dual polytope
The dual polytope of an n-orthotope has been variously called a rectangular n-orthoplex, rhombic n-fusil, or n-lozenge. It is constructed by 2n points located in the center of the orthotope rectangular faces.
An n-fusil's Schläfli symbol can be represented by a sum of n orthogonal line segments: { } + { } + ... + { }.
A 1-fusil is a line segment. A 2-fusil is a rhombus. Its plane cross selections in all pairs of axes are rhombi.