Are we an intersection?

One of my IB Maths assignments was called "How many pieces?" and its purpose was to investigate the maximum number of pieces obtained after we applied n cuts to a t-dimensional object. For example, for the simplest case of a 1-dimensional object (a line), each new cut will lead to one new piece. It was one of the most interesting projects I have complete till now and I have come up with some really challenging ideas. One of them can be put as a simple question:

Are we an intersection?

Imagine a 2-dimensional space. Now imagine two straight lines (1-dimensional objects) intersecting each other. They intersect at one point we call point of intersection and which is a 0-dimensional object.Now follow the same line of thought but in a 3-dimensional space. Imagine two planes (2-dimensional objects) intersecting each other. They intersect at a straight line we will call straight line of intersection and which is a 1-dimensional object.We can extrapolate these results and table them.

Space Dimension	Objects Dimension	Intersection Dimension
2	1	0
3	2	1
4	3	2
5	4	3
...	...	...
n+2	n+1	n

Actually, the fourth row is the important one for this post. Our senses can only detect 3 dimensions, no more, no less, which makes us to believe (even though there is the possibility of that not being the truth) that the Universe is made of 3 dimensions.

If we observe the fourth row of the table, we see that the intersection dimension corresponds to exactly 3 dimensions. And now we reach the main point of this post!

Following this reasoning, the conclusion for this post is:

Our Universe might be the intersection between two four-dimensional Universes, in a fifth-dimensional space.

This thought opens the chance of the existence of other Universes similar to ours, resulting from the intersection of two other fourth-dimensional Universes.