The hypercube does not exist in real life. A 4th-spatial-dimension is purely mathematical.
We are 3-dimensional beings. The actual, existing 4th dimension is time. However that is not my focus.
I am intrigued by the concept of the physical transformation from 3D objects to 4D objects. Similar to 2D to 3D.
This animation shows the process in which the hypercube can be understood. As the number of dimensions increase, # of sides, vertices and volume increase.
| Dimension | # Sides | # Vertices | Volume | Description |
| 0 | 0 | 1 | 4^0 = 0 | It's a point. It has no volume, 0 dimensions. Does it even exist? |
| 1 | 2 | 2 | 4^1 = 4 | This, ladies and gentlemen, is a line. It has a length of 4. It is the distance between two points. |
| 2 | 4 | 4 | 4^2 = 16 | The square has a surface area. It is important to note that each side is the whole object from the previous dimension. |
| 3 | 6 | 8 | 4^3 = 64 | Welcome to cube life! This has a total of 6 squares as its sides. Two sides centered directly on the x, y, and z axis. |
| 4 | 8 | 16 | 4^4 = 256 | Alas! The hypercube has appeared (through matematics). Each sides (now 8 cubes) centered on x, y, z, and w axes. |
An excellent movie which shows the relationship between 2D and 3D is Flatland. When attempting to understand the relationship from 3D and beyond, knowing the basics of 2D to 3D is very helpful. Click here to learn about 2D to 3D.