An n-dimensional unit hypercube is a shape whose vertices are all the n-dimensional points whose coordinates are either 0 or 1.
For example the 2-dimensional unit hypercube with vertices at (0,0), (1,0), (0,1) and (1,1) is a square. The square has 4 vertices and 4 edges.
The 3-dimensional unit hypercube with vertices at (0,0,0), (1,0,0), (0,1,0), (0,0,1), (1,1,0), (1,0,1), (0,1,1), (1,1,1) is a cube.
The 4-dimensional unit hypercube with vertices at (0,0,0,0), (1,0,0,0), …, (0,1,1,1), (1,1,1,1) is a tesseract.