Hyperrectangle

In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, a hyperrectangle (also called a box, hyperbox, 
 
 
 
 k
 
 
 {\displaystyle k}
 
-cell or orthotope), is the generalization of a <a href="/facts/Rectangle/mdLfIGKA">rectangle</a> (a <a href="/facts/Plane_figure/nww0x85d">plane figure</a>) and the <a href="/facts/Rectangular_cuboid/eLLKX4rh">rectangular cuboid</a> (a <a href="/facts/Solid_figure/tHH3JFoq">solid figure</a>) to <a href="/facts/Higher_dimension/0ktmUyac">higher dimensions</a>. A <a href="/facts/Necessary_and_sufficient_condition/G45aDCY9">necessary and sufficient condition</a> is that it is <a href="/facts/Congruence_(geometry)/2tKJ6AhB">congruent</a> to the <a href="/facts/Cartesian_product/BfqBWzdL">Cartesian product</a> of finite <a href="/facts/Interval_(mathematics)/e9se3vTe">intervals</a>. This means that a 
 
 
 
 k
 
 
 {\displaystyle k}
 
-dimensional rectangular solid has each of its edges equal to one of the closed intervals used in the definition. Every 
 
 
 
 k
 
 
 {\displaystyle k}
 
-cell is <a href="/facts/Compact_(mathematics)/d0cgXJH7">compact</a>.
If all of the edges are equal length, it is a <a href="/facts/Hypercube/q2mRPbIz">hypercube</a>. A hyperrectangle is a special case of a <a href="/facts/Parallelohedron/4B0xFmsg">parallelotope</a>.

Hyperrectangle open-in-new

Hyperrectangle