trigonometry-is-my-bitch:

Geometrical visualisation of a 4D shape from a 3D Perspective - The Tesseract

Hypercubes are shapes with n dimensions where n is greater than the 3 dimensions of a normal cube. The Tesseract, or the 4-cube, is a 4 dimensional hypercube.

where n is the dimensional number, in any hypercube:

vertices = 2^n

edges = n(2^n-1 )

faces = 2^n-3(n-1)n