## Building a Corral in 4D

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

### Building a Corral in 4D

Let's build a corral in ordinary 3D. A circle encloses the maximum amount of ground for the amount of material used to build it. To build one, you first draw a big circle on the ground. Set posts into that circle at regular intervals. Connect the posts with slats. Done.

In 4D you draw a sphere on the ground. Set posts into that sphere at regular intervals. Oops, that is only possible with certain numbers. The only real possibility is twenty, but that might be too small. So what should 4D ranchers do?

When building it is always desirable to have standardized parts. We want all the slats to be the same length. We usually can't do that, but maybe it is possible to have two standard lengths. Anyone know how?
PatrickPowers
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### Re: Building a Corral in 4D

Well, you could use a disdyakis triacontahedron (a catalan solid with 120 identical scalene triangular faces) as the shape of your corral.
Mecejide
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### Re: Building a Corral in 4D

A geodesic dome works quite well as well, those triangles are similar enough for all practical purposes
student91
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### Re: Building a Corral in 4D

Now that I think about it, there's no reason the corral needs to be convex, so that opens up a few more options.
Mecejide
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### Re: Building a Corral in 4D

student91 wrote:A geodesic dome works quite well as well, those triangles are similar enough for all practical purposes

So it is. It needn't be a Platonic solid. I'm surprised it's that easy.
PatrickPowers
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### Re: Building a Corral in 4D

Mecejide wrote:Now that I think about it, there's no reason the corral needs to be convex, so that opens up a few more options.

Gotta be convex. The whole point is to enclose maximal area with minimal materials. Not many trees in the desert.
PatrickPowers
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### Re: Building a Corral in 4D

I don't think you can use slates in 4d in the first place. Slates are fundamentally 1d. But in 4d your boundary is a sphere and not a circle. So you have to use some kind of 2d tiling, with cavities that are small.
Like slates, these 2d tiling would then be stacked into the height dimension with empty space in between.
DonSoreno
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### Re: Building a Corral in 4D

It is only needing to be convex if you don't have to funnel your animals for individual attention. I've been in a number that were not convex.

The corral can be made as a log arrangement, as long as there is no place for an animal to pass through.
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