An n-dimentional analogue of a square is called an n-cube, or a hypercube. They can be constructed by numbering the vertices using n base-2 bits.
n = 0
A 0-cube is just a point.
n = 1
A 1-cube is a line. Its vertices can be labeled using 1 bit.
n = 2
A 2-cube is a square. Its vertices can be labeled using 2 bits.
n = 3
A 3-cube is a cube. Its vertices can be labeled using 3 bits.
n = 4
A 4-cube is a tesseract. Its vertices can be labeled using 4 bits. This is where binary labeling of vertices can be especially useful, because it can help construct a tesseract.
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