Английская Википедия:Hyperrectangle
Шаблон:Short description Шаблон:Infobox polyhedron
In geometry, a hyperrectangle (also called a box, hyperbox, or orthotope[1]), 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. If all of the edges are equal length, it is a hypercube. A hyperrectangle is a special case of a parallelotope.
Types
A four-dimensional orthotope is likely a hypercuboid.[2]
The special case of an Шаблон:Mvar-dimensional orthotope where all edges have equal length is the Шаблон:Mvar-cube or hypercube.[1]
By analogy, the term "hyperrectangle" can refer 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.[3]
Dual polytope
The dual polytope of an Шаблон:Mvar-orthotope has been variously called a rectangular Шаблон:Mvar-orthoplex, rhombic Шаблон:Mvar-fusil, or Шаблон:Mvar-lozenge. It is constructed by Шаблон:Math points located in the center of the orthotope rectangular faces.
An Шаблон:Mvar-fusil's Schläfli symbol can be represented by a sum of Шаблон:Mvar orthogonal line segments: Шаблон:Math or Шаблон:Math
A 1-fusil is a line segment. A 2-fusil is a rhombus. Its plane cross selections in all pairs of axes are rhombi.
| Шаблон:Mvar | Example image |
|---|---|
| 1 | Файл:Cross graph 1.svg Line segment Шаблон:Math Шаблон:CDD |
| 2 | Файл:Rhombus (polygon).png Rhombus Шаблон:Math Шаблон:CDD |
| 3 | Файл:Dual orthotope-orthoplex.svg Rhombic 3-orthoplex inside 3-orthotope Шаблон:Math Шаблон:CDD |
See also
Notes
References
External links
- ↑ 1,0 1,1 Coxeter, 1973
- ↑ http://ui.adsabs.harvard.edu/abs/2022arXiv221115342H/abstract
- ↑ See e.g. Шаблон:Citation.
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