Hypercubes.
The animation shows the progression of cubes from zero dimensions through seven dimensions.
A zero-dimensional cube is simply a point.
A 1-dimensional cube is a line segment.
2D cube is a square.
3D cube is a cube.
4D - tesseract.

What are the names of the hyper cubes for dimensions 5, 6, and 7? Go online. You should be able to find names up through 12 dimensions.
What are the next five elements in the progression of vertices? (1, 2, 4, 8, ....) What is the formula for determining the next element?
What are the next five elements in the progression of edges? (0, 1, 4, 12, 23, ....) What is the formula for determining the next element?
What are the next five elements in the progression of square faces? (0, 0, 1, 6, 24, 80, ....) What is the formal for determining the next element?
What are the next five elements in the progression of cubic faces? (0, 0, 0, 1, 8, 40, 160, ....) What is the formal for determining the next element?
What is the general formula that applies to all of the progressions?