Hyperrectangle

Hyperrectangle
Orthotope
A rectangular cuboid is a 3-orthotope
TypePrism
Faces2n
Edgesn × 2n1
Vertices2n
Schläfli symbol{}×{}×···×{} = {}n
Coxeter diagram···
Symmetry group[2n−1], order 2n
Dual polyhedronRectangular n-fusil
Propertiesconvex, zonohedron, isogonal

In geometry, a hyperrectangle (also called a box, hyperbox, -cell or orthotope), is the generalization of a rectangle (a plane figure) and the rectangular cuboid (a solid figure) to higher dimensions. A necessary and sufficient condition is that it is congruent to the Cartesian product of finite intervals. This means that a -dimensional rectangular solid has each of its edges equal to one of the closed intervals used in the definition. Every -cell is compact.

If all of the edges are equal length, it is a hypercube. A hyperrectangle is a special case of a parallelotope.