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# Hyperrectangle  ( Polytopes )

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A rectangular is a 3-orthotope
Prism
2 n
2 n
{} × {} ... × {}N.W. Johnson: Geometries and Transformations, (2018) Chapter 11: Finite symmetry groups, 11.5 Spherical Coxeter groups, p.251
...
2 n−1, order 2 n
Rectangular n-fusil
convex, ,
In , an orthotopeCoxeter, 1973 (also called a hyperrectangle or a box) is the generalization of a to higher dimensions. It is formally defined as the Cartesian product of intervals. A hyperrectangle is a special case of a parallelotope.

Types
A three-dimensional orthotope is also called a right rectangular prism, rectangular , or rectangular .

The special case of an n-dimensional orthotope where all edges have equal length is the n-.

By analogy, the term "hyperrectangle" or "box" can refer to Cartesian products of intervals of other kinds, such as ranges of keys in or ranges of , rather than .See e.g. .

Dual polytope

Example: 3-fusil
2 n
2 n
{} + {} + ... + {}
...
2 n−1, order 2 n
n-orthotope
convex,
The of an n-orthotope has been variously called a rectangular n-, rhombic n-fusil, or n-. It is constructed by 2 n points located in the center of the orthotope rectangular faces.

An n-fusil's Schläfli symbol can be represented by a sum of n orthogonal line segments: { } + { } + ... + { }.

A 1-fusil is a . A 2-fusil is a . Its plane cross selections in all pairs of axes are .

Notes

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