-cube is a generalization of a cube where 0-cube is a vertex, 1-cube is a line segment, 2-cube is a square, 3-cube is a cube and 4-cube is a hypercube. -cube has its -faces where 0-faces are vertexes, 1-faces edges and 2-faces are faces.
Ever wondered how many -faces does an -cube have? It is easy to calculate with the following hint as a starting point. Consider a cube with points . What is the necessary and sufficient condition on the coordinate values of the four points of a cube to form a face?
Afterwards, you should obtain a formula:
The number of -faces of -cube is .