hyperrectangle
Sign in to saveAlso known as box, n-orthotope
thumb|Projections of k-cells onto the plane (from k\in\{1,\dots{},6\}). Only the edges of the higher-dimensional cells are shown. In geometry, a hyperrectangle (also called a box, hyperbox, k-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 k-dimensional rectangular solid has each of its edges equal to one of the closed intervals used in the definition. Every k-cell is compact.
Key facts
- Polyhedron.name
- -fusil
- Polyhedron.image
- File:Rhombic 3-orthoplex.svg
- Polyhedron.caption
- Example: 3-fusil
- Polyhedron.type
- Prism
- Polyhedron.schläfli
- {{math|1={}+{}+···+{} = {} }}
- Polyhedron.coxeter
- ...
- Polyhedron.symmetry
- , order
- Polyhedron.dual
- -orthotope
- Polyhedron.properties
- convex, isotopal
via Wikipedia infobox
~4 min read
Article
8 sectionsContents
- Formal definition
- Intuition
- Types
- Dual polytope
- See also
- Notes
- References
- External links
{{Infobox polyhedron | name = HyperrectangleOrthotope | image = Cuboid no label.svg | caption = A rectangular cuboid is a 3-orthotope | type = Prism | faces = | edges = | vertices = | vertex_config = | schläfli = {{math|1={}×{}×···×{} = {}n}} | wythoff = | conway = | coxeter = ··· | symmetry = , order | rotation_group = | surface_area = | volume = | angle = | dual = Rectangular -fusil | properties = convex, zonohedron, isogonal }} thumb|Projections of k-cells onto the plane (from k\in\{1,\dots{},6\}). Only the edges of the higher-dimensional cells are shown. In geometry, a hyperrectangle (also called a box, hyperbox, k-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 k-dimensional rectangular solid has each of its edges equal to one of the closed intervals used in the definition. Every k-cell is compact.
If all of the edges are equal length, it is a hypercube. A hyperrectangle is a special case of a parallelotope.