A representation of a 4D object in 3D space

A square has 4 corners, a cube has 2 x 4 = 8 corners, and a tesseract has 2 x 8 = 16 corners.

A square has 4 edges, a cube has 2 x 4 + 4 = 12 edges, and a tesseract has 2 x 12 + 8 = 32 edges. (Here the +4 comes from the fact that a square has 4 corners, and the +8 comes from the fact that a cube has 8 corners.)

A square has 1 square, a cube has 2 x 1 + 4 = 6 squares, and a tesseract has 2 x 6 + 12 = 24 squares. (Here the +4 comes from the fact that a square has 4 edges, and the +12 comes from the fact that a cube has 12 edges.)

A cube has 1 cube, and a tesseract has 2 x 1 + 6 = 8 cubes. (Here the +6 comes from the fact that a cube has 6 squares.)