What is a hypercube?
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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.

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