Editing Hypercube (section)

=== By the number of dimensions ===
[[File:From Point to Tesseract (Looped Version).gif|thumb|An animation showing how to create a tesseract from a point.]]

A hypercube can be defined by increasing the numbers of dimensions of a shape:
:'''0''' – A point is a hypercube of dimension zero.
:'''1''' – If one moves this point one unit length, it will sweep out a line segment, which is a unit hypercube of dimension one.
:'''2''' – If one moves this line segment its length in a [[perpendicular]] direction from itself; it sweeps out a 2-dimensional square.
:'''3''' – If one moves the square one unit length in the direction perpendicular to the plane it lies on, it will generate a 3-dimensional cube.
:'''4''' – If one moves the cube one unit length into the fourth dimension, it generates a 4-dimensional unit hypercube (a unit [[tesseract]]).

This can be generalized to any number of dimensions. This process of sweeping out volumes can be formalized mathematically as a [[Minkowski sum]]: the ''d''-dimensional hypercube is the Minkowski sum of ''d'' mutually perpendicular unit-length line segments, and is therefore an example of a [[zonotope]].

The 1-[[Skeleton (topology)|skeleton]] of a hypercube is a [[hypercube graph]].