Hyperrectangle
| Hyperrectangle Orthotope | |
|---|---|
A rectangular cuboid is a 3-orthotope | |
| Type | Prism |
| Faces | 2n |
| Edges | n × 2n−1 |
| Vertices | 2n |
| Schläfli symbol | {}×{}×···×{} = {}n |
| Coxeter diagram | ··· |
| Symmetry group | [2n−1], order 2n |
| Dual polyhedron | Rectangular n-fusil |
| Properties | convex, 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.