Take six cubes and arrange them into the shape of a crucifix. Take two more cubes and stick them on either side of the crucifix, at the point where the cross is made. Now you have a tesseract.
We are all familiar with the terms 2-D and 3-D many times which represent two-dimensional and three-dimensional objects in space respectively.
However, what do those dimensions really mean?
What is Dimension
A dimension is a direction in which you can go. When drawing a line on a piece of paper we can go up and down the y-axis as well as the left and right x-axis which means that a piece of paper is two-dimensional as there are only two directions we can go in.
How to Visualize 4 dimension
Now in reality we can also go in and out which provides a sense of depth in three-dimensional space. A dot is equivalent to zero dimensions a line represents one dimension and square has two dimensions and a cube has three. Now take a three dimension cube and replace each face which is currently a square with a cube the shape you now hold is a four-dimensional tesseract. Basically, a tesseract is a cube that exists in four-dimensional space or the 4d analog of a cube.
The visualization is not 4 dimensional rather it is a representation of 4 dimensions in 3 dimensions and then it is rendered in a 2-dimensional screen
Here is a simple way to conceptualize dimensions. A Square is a 2d shape so each of its corners has two lines coming off it at 90 degrees. A cube is three-dimensional so each of its corners has three lines coming from it. Similarly, a tesseract is a 4d shape so every corner has four lines coming off it.
Since humans have only evolved to visualize the world in three dimensions anything that’s a part of further dimensions like 4d, 5d, or 6d doesn’t make much sense to us because we can’t visualize them our brains can’t make any sense of a fourth dimension in space. We simply can’t wrap our heads around it. However just because we can’t visualize a concept doesn’t mean that it can not exist.
Mathematically, a tesseract is a perfectly accurate and plausible shape as are all shapes in higher dimensions such 5d and 6d. Just as a cube can be unfolded into 6 squares in two-dimensional space a tesseract can be unfolded into 8 cubes in three-dimensional space that might be a bit mind-blowing but don’t worry math checks out and this concept will continue to fascinate mathematicians and engineers.