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The Tesseract assumes that in order to add another Euclidean dimension another orthogonal plane is added into the mix, right? That is the pattern when going from 1D to 2D to 3D, but it seems like something slightly different is going on from 0d to 1D. From a point to a line - a radial line is orthogonal to a circle, but 0D is not a really a circle, it's a point, so from 0D to 1D, it doesn't really seem like adding on an orthogonal plane (what is orthogonal to a point? everything? nothing?) instead, it makes sense to me that a line is created by an infinite number of points. Following that pattern -

0D-1D: line is an infinite number of points

1D-2D: plane is an infinite number of lines

2D-3D: 3D is an infinite number of planes

3D-4D: 4D is an infinite number of 3D spaces? like a bunch of cubes stacked on top of one another or something?

Has anyone else submitted anything other than a Tesseract to represent 4D?

Also, how would you describe going from 0D to 1D?

Thanks!

(sorry if this is the wrong place to post this, I thought I saw another higher dims thread over here, so hopefully this is ok!)