Hypercubes.[br][br]The animation shows the progression of cubes from zero dimensions through seven dimensions. [br][br]A zero-dimensional cube is simply a point.[br]A 1-dimensional cube is a line segment.[br]2D cube is a square.[br]3D cube is a cube.[br]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.[br]What are the next five elements in the progression of vertices? (1, 2, 4, 8, ....) What is the formula for determining the next element?[br]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?[br]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?[br]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?[br]What is the general formula that applies to all of the progressions?