Editing Tesseract (section)

===Coordinates===

A ''unit tesseract'' has side length {{math|1}}, and is typically taken as the basic unit for [[hypervolume]] in 4-dimensional space. ''The'' unit tesseract in a [[Cartesian coordinate system]] for 4-dimensional space has two opposite vertices at coordinates {{math|[0, 0, 0, 0]}} and {{math|[1, 1, 1, 1]}}, and other vertices with coordinates at all possible combinations of {{math|0}}s and {{math|1}}s. It is the [[Cartesian product]] of the closed [[unit interval]] {{math|[0, 1]}} in each axis.

Sometimes a unit tesseract is centered at the origin, so that its coordinates are the more symmetrical <math>\bigl({\pm\tfrac12}, \pm\tfrac12, \pm\tfrac12, \pm\tfrac12 \bigr).</math> This is the Cartesian product of the closed interval <math>\bigl[{-\tfrac12}, \tfrac12\bigr]</math> in each axis.

Another commonly convenient tesseract is the Cartesian product of the closed interval {{math|[&minus;1, 1]}} in each axis, with vertices at coordinates {{math|(±1, ±1, ±1, ±1)}}. This tesseract has side length 2 and hypervolume {{math|1=2<sup>4</sup> = 16}}.