(some ideas here are mine, and I'm really not an expert about these dimensions, so please, please take them with a grain of salt)

Part 1 ended with a confusing hypercube

So this time let's just look at what we know best- dots, lines, squares and cubes.

Hypercubes won't come out today(except for the very end, a tiny role.)

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This form counts the number of dots, lines, squares and cubes in... a dot, line, square and a cube.

To make explaining easier, I'll call each of the components x-D components (a dot will be 0-D, lines are 1-D, squares are 2-D and so on)

For example, a square is made from four 0-D components (dots), four 1-D components (lines) and one 2-D component (square). Get the idea?

As you can see, the number of 0-D components always gets multiplied by 2 every time there's a new dimension.

This is because, adding a new dimension means you slide the shape from one dimension back to another direction. (e.g. to make a square, you slide a line in the direction of the Y-axis)

So when you think about it, it's natural that the number of dots gets multiplied every time there's a new dimension.

With that info, let's look at the number of dots in hypercube(you know, this one)

yep, it IS 8 x 2=16 dots!!

So next time, let's look at this hypercube with the number of dots, lines, ...(i hate having to have to keep repeating this)

... well, components, in short.

I think I've got a pretty good idea.