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What is "verticy"? A plane is like a paper, isn't it?

Imagine you have two squares, one is standing on its side while another is on the ground. If you put the first square on top of the second doesn’t it’s intersection create a line? Planes are infinite 2d spaces. If you lay them out like I described then you have what you described.

Ok. I just grabbed two post-its to try. How should I put them together, like stacking? or put one flat on the table and the other vertically on it? But if viewed from above, that's still a square, not a line? what am I doing wrong mate

Also it could only be a 2d plane because a 3d tensor would leave a 2d shadow, and a 2d plane would leave a 1d shadow. A 1d shadow is a line.

2d objects have no thickness a 2d observer would only see a line.

Ok, that last comment surprisingly makes sense. So it is impossible for a higher dimensional thingy to leave a 1d shadow, right? so I cannot have an infinite something that looks like a line in 2D?

wait, I am confused again

You could have a 2d plane intersecting at a different verticy.

Does that make sense?

Ok, here's how I put the post-its.
If I look down, it looks like a square not a line. And what is "verticy"? My dictionary does not have it

If I look at the post-its, it seems impossible

That is because you are seeing it from 3d. If you were to put ink on one of the edges and layer it on the other edge on the other you would leave a line. This is what would essentially be a shadow on a 2d plane. If that makes sense.

Copied from Khan academy
A vertex is a point where two straight lines or rays meet. Vertices are found in angles, which are measured in degrees. They're also found in two-dimensional and three-dimensional objects where the sides or edges of these objects meet.

https://en.wikipedia.org/wiki/Plane–plane_intersection

Ok, so verticity means putting things together? Vertex is the point where two things meet?
As for putting ink, did I put the post-it notes correctly or should I hold them differently? Would I put the ink on the first or the second note?

So don’t put ink on the one lying on the table, put it on the one you put on top of it, and yes you did it correctly.

Wikipedia link is very good! I think I know what you were saying now - let's hope I actually do this time:
To have infinite dimensional line, I need infinite planes to intersect?

Put it on the edge that touches the other note.

Yes infinite planes for infinite lines.

Thank you for your patience and explaining something this complex to a loggerhead like me!