Hypercube

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• Take a dot (zero dimensional object) and move it any direction.
• Result is a straight line - called the 1-cube.

• Take a straight line (one dimensional object) and move it, the same distance, in a direction orthogonal to the first direction.
• Result is a square - called the 2-cube.

• Take a square (two dimensional object) and move it, the same distance, in a direction orthogonal to both the first two directions.
• Result is a cube - called the 3-cube.

• Take a cube (three dimensional object) and move it, the same distance, in a direction orthogonal to all the other directions !!!
• Result a Tesseract - called the 4-cube.

This procedure results, at each stage, in the hypercube for that dimension or n-dimensional hypercube or n-cube.

• http://en.wikipedia.org/wiki/Hypercube
• http://mathworld.wolfram.com/Hypercube.html