I get 1, 2, and 3 dimensions and their visual representations. For instance, 3-dimensional space has width, length, and depth but how about a 6-dimensional space, how can we grasp it in n intuitive manner free of mathematical analysis?
In: 8
Lets talk about Nets.
In geometry, a Net is an unfolded 3D shape.
Imagine you’ve made a cube out of paper.
It’s six squares (2D shapes) joined on the edges and folded 90 degrees to create a 3D cube.
A Tesseract is a 4D cuboid. Basically the next one up.
A Tesseract’s Net is eight cubes, joined on their faces and folded onto one another, as a Net (called a Dali Cross in this case) it looks a bit like a minecraft tree, but fully constructed into a 4D shape the eight cubes all link together. Every face of every cube connects to the face of another cube. That might be a little hard to visualise, but Wikipedia has a rather nice animation of a rotating Tesseract which illustrates it.
If you were inside a hollow tesseract and traversing it as a 3D person, you’d be able to travel in a straight line through four cubic volumes before coming back to where you started. This applies whichever direction you pick.
A 5D Hypercube would be something like 10 tesseracts joined across their individual 3D cube-volumes, folded around so they link together into a single shape.
A 6D Hypercube would be 12 5D Hypercubes joined across their Tesseract volumes.
Basically it’s an X dimensional shape composed of a set of X-1 Dimensional objects, joined across their X-2 connections.
I have no idea how to describe what a 5D or 6D Hypercube would look like, only that if it were a hollow shape and you could traverse it in 3D, you’d be hopelessly lost very very quickly.
Perceived from a 3D perspective, it’d be either a ridiculously wibbly shape that in no way resembles a cube (most likely some kind of spike-ball) or an impossibly complex maze of cubic volumes.
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