Editing Cube (section)

== Construction ==
[[File:The 11 cubic nets.svg|thumb|Nets of a cube]]
An elementary way to construct is using its [[Net (polyhedron)|net]], an arrangement of edge-joining polygons, constructing a polyhedron by connecting along the edges of those polygons. Eleven nets for the cube are shown here.{{r|jeon}}

In [[analytic geometry]], a cube may be constructed using the [[Cartesian coordinate systems]]. For a cube centered at the origin, with edges parallel to the axes and with an edge length of 2, the [[Cartesian coordinates]] of the vertices are <math> (\pm 1, \pm 1, \pm 1) </math>.{{r|smith}} Its interior consists of all points <math> (x_0, x_1, x_2) </math> with <math> -1 < x_i < 1 </math> for all <math> i </math>. A cube's surface with center <math> (x_0, y_0, z_0) </math> and edge length of <math> 2a </math> is the [[Locus (mathematics)|locus]] of all points <math> (x,y,z) </math> such that
<math display="block"> \max\{ |x-x_0|,|y-y_0|,|z-z_0| \} = a.</math>

The cube is [[Hanner polytope]], because it can be constructed by using [[Cartesian product]] of three line segments. Its dual polyhedron, the regular octahedron, is constructed by [[direct sum]] of three line segments.{{r|kozachok}}