A zero-dimensional object is known as a node, simply a point in space. A one-dimensional object,
such as an axis made up of a straight line of nodes, is known as an edge. The first dimension can
be considered to have length, but not width. When a second dimension is added, the result is a
plane, such as is considered in fundamental mathematics where one axis is labeled X, and the
other Y. A third dimension results when a plane of two dimensions has an additional axis, known
as the Z axis. Each additional axis expands the ability to categorize a location in space. The
universe that we perceive is made up of three physical dimensions. A hypercube is the concept of
a cube, a three-dimensional object that is expanded at least one dimension, to a fourth
dimension. Since the third-dimension is the limit of being able to plot a cube physically,
other concepts are implemented in order to conceptualize a cube of four-dimensions, or more. A
4-cube is often represented as a cube inside a cube, where each corner of each of the
three-dimensional cubes is connected by a single line. The reason for representing a 4-cube
this way is much the same reason that a three-dimensional cube is represented is many
two-dimensional parallel planes. Each plane is in instance of a location of the Z axis; for
instance, the location (X,Y,Z) = (2,3,4) is the location (2,3) on the (X,Y), at the instance
"4" on the Z axis. A value on the additional dimension is always considered an instance on
the new axis of the previous axis. In the case of a 4-cube, the cube on the outside, and the
cube on the inside, are instances of a third-dimension cube in the fourth dimension. This
simple representation is a simplified concept of what the fourth dimension. In order to
explain what is being observed, note that a one-dimensional line has a length of infinity
in both directions. Additionally, a two-dimensional plane is made up of an infinite number
of parallel lines. Theoretically, this would be depicted as a sheet of nodes so tightly
packed that what would be seen is a horizon. Again, theoretically, the third-dimension
would realistically be depicted as a infinite number of parallel sheets, where no structure
could be represented. In order to simplify the representation, a third-dimensional cube is
represented as the third dimension. This, and the 4-cube described above are the minimum
representation of the third and fourth dimension respectfully. Thus, a 4-cube could be
represented as a cube inside a cube connected at its corners, or it could be represented
as a cube next to another cube, connected at the same corners. Hypercubes of dimensions
greater than 4 more difficult to depict due to the limitation of representation in our
three dimensional lives. There are numerous applications for physical dimensions greater
than three, but are represented in less physical ways.