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.