Back Hyperrechteck German Υπερορθογώνιο Greek Hiperrectángulo Spanish Iperrettangolo Italian 超直方体 Japanese Hyperrechthoek Dutch Przedział wielowymiarowy Polish Гиперпрямоугольник Russian Гіперпрямокутник Ukrainian
| Hyperrectangle Orthotope | |
|---|---|
 A rectangular cuboid is a 3-orthotope | |
| Type | Prism |
| Faces | 2n |
| Edges | n × 2n−1 |
| Vertices | 2n |
| Schläfli symbol | {}×{}×···×{} = {}n[1] |
| 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[2]), 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.[3] 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.[4][5]
If all of the edges are equal length, it is a hypercube. A hyperrectangle is a special case of a parallelotope.
- ^ N.W. Johnson: Geometries and Transformations, (2018) ISBN 978-1-107-10340-5 Chapter 11: Finite symmetry groups, 11.5 Spherical Coxeter groups, p.251
- ^ Coxeter, 1973
- ^ Foran (1991)
- ^ Rudin (1976:39)
- ^ Foran (1991:24)