Hyperrectangle

For every integer i from 1 to k, let a_i and b_i be real numbers such that a_i . The set of all points x=(x_1,\dots,x_k) in \mathbb{R}^k whose coordinates satisfy the inequalities a_i\leq x_i\leq b_i is a k-cell. == Intuition ==

A k-cell of dimension k\leq 3 is especially simple. For example, a 1-cell is simply the interval [a,b] with a . A 2-cell is the rectangle formed by the Cartesian product of two closed intervals, and a 3-cell is a rectangular solid. The sides and edges of a k-cell need not be equal in (Euclidean) length; although the unit cube (which has boundaries of equal Euclidean length) is a 3-cell, the set of all 3-cells with equal-length edges is a strict subset of the set of all 3-cells. ==Types==

A four-dimensional orthotope is likely a hypercuboid. The special case of an -dimensional orthotope where all edges have equal length is the -cube or hypercube. ==Dual polytope==

The dual polytope of an -orthotope has been variously called a rectangular -orthoplex, rhombic -fusil, or -lozenge. It is constructed by points located in the center of the orthotope rectangular faces. An -fusil's Schläfli symbol can be represented by a sum of orthogonal line segments: {{math|{ } + { } + ... + { } }} or {{math|n{ }.}} A 1-fusil is a line segment. A 2-fusil is a rhombus. Its plane cross selections in all pairs of axes are rhombi. ==See also==