Summary of unique properties of all dimensions?

[Secret]

Trying to look in the teamikaria wiki found nothing about unique features of the various dimensions
Trying to look into alkaline's pages yield only a fraction of the unique properties of 4D
Checking various websites out there yield similar results.

Can someone post a full list of unique features or properties of the various dimensions here so that it can be used as a convenient reference for higher dimensional investigation and exploration?

E.g. Knots are impossible in dimensions < 2
Clifford parallels are possible in dimensions > 3
Exotic Rⁿ exist only for n = 4

[wendy]

Not really.

One has to go out to the dimension to see what's there. 124 dimemsions seems rather interesting, as does 5, 8, 6, 24, and a couple of others.

3d is the only dimension where stable elliptical orbits exist.

clifford parallels exist only in even dimensions, because only even dimensions support a smooth hairy ball.

There are interesting things in all of the dimensions, but it takes some time to find them.

[anderscolingustafson]

I know that 2d is the only number of dimensions were there can be an infinite number of regular solids. It's also the only number of dimensions were you can fold up an object without bending it's sides. In 3d if you try folding up a cube for instance you will bend some of it's square faces but in 2d you can fold up a square without bending any of it's square sides.

1d is the only number of dimensions were energy cannot disperse and distance from an object has no effect on how bright it is. It's also the only number of dimensions were only one shape is possible.

3d is the smallest number of dimensions were weaving and tying knots is possible. It's also the smallest number of dimensions were you can have a hole going strait threw an object without dividing it in two. 3d is also the only number of dimensions were compasses could work using magnetism alone. In 2d a compass would be pointless as the ground would be a line. In 4d a compass could be used to determine North and South assuming stable 4d physics but it would be useless for determining East-West and Marp-Garp as the arrows not pointing to either pole could spin around freely. 3d is also the only number of dimensions were lines such as wires and hair can get tangled. In 2d lines can't get tangled because knots are impossible wile lines in 4d would be equivalent to points in 3d.

4d is the smallest number of dimensions were sponges can move threw each other. It is also the smallest number of dimensions were there can be rings that are basically perpendicular but with all points on each ring equally distant from every other ring. 4d is also the smallest number of dimensions were going around rivers instead of crossing them is possible. It is also the only number of dimensions were the polar equator and solar equator of a planet would have the same number of dimensions. 4d is also the smallest number of dimensions were one could circumnavigate a continent.

5d is the smallest number of dimensions were there can be only three regular solids.

I hope this helps.

[Keiji]

I've written up a new Dimensional Features Summary, incorporating ideas from this thread and other things I remembered.