Exploring Other Directional Systems

What?

English (and I think most other languages but I haven't bothered to check) use an axial directional system, where we have names for the 6 cardinal directions 90 degrees apart. Forward, backward, left, right, up, and down. But I was thinking... there's probably other systems you could use, too. Probably less convienent, but none the less cool.

Pentagonal Directions

My first idea was a pentagonal directional system. There's lots of different ways we could orient this pentagon, but I think the most sense is to have a vertex pointed forward. As this is a 2D shape, we'd still have up and down, but then we wouldn't have backward, left, and right. Here's the names I made up.

These are obviously very silly and I thought of these names in less than 6 minutes. The point is not to create a good system, but just to showcase what could be done. Same goes for all of the following systems.

Merging Directions

"It's in the top left drawer"

"The statue was just in front of me, to my left"

"The six dimensional axolotl was in front of me, but its attention was fixed at something to the right and ana of where I was standing, plus some rotation into the fifth or sixth dimension."

These are all completely normal sentences (except that four dimensional creature's run in with my pet), because we don't just use left/right/up/down/forward/back, we mix them. Mixing direction names is super helpful, because it doubles your direction count and costs 0 new words! So the pentagonal system is really a decagonal system, and our system is really octagonal (both examples ignoring height).

Regular Polygons

Something interesting about regular polygons is that they have the symmetry of the factors of their number of sides. In a way, regular polygons are like a physical manifestation of integers greater than 2, and I think that's really cool. Like how primes don't have any symmetry except their own.

Notice how every regular polygon with an even number of sides has opposite corners and opposite edges? This is because they have the symmetry of the imaginary 2 sided polygon, or an edge. 6 is 2*3, and hexagons have 2 way axis symmetry, and 3 way triangular symmetry. Super cool!

Hexagonal Directions

This will be slightly more convienent, since hexagons are even and have opposite sides. But still not great since there's not names for directions 90 degrees apart. Directional systems should be based off of polygons divisible by four. (In order to be good, anyway)

As I said previously, we can merge directions. In this case, merging directions gets us to something usable, since 12 is divisible by four. So if a culture were to use this hexagonal system, instead of saying left and right, they'd say kesh kalsh, and pesh palsh. Very inconvienent.

Triangular Directions

Oops totally forgot that polygons simpler than squares exist. Here's triangular directions. It's basically just hexagonal directions but without those pesky extra directions making it usable.

Heptagonal Directions

Another prime polygon. This makes it really bad to use, but pretty! For this one I put a bit of thought into the phonetics. All of the left directions end in an open sound, like a vowel, and all of the rights end in a harsh consonant, like a stop/plosive. Lastly, the two backward directions each begin with "b".

Octagonal Directions

This would just be our system but with names for the diagonals. I'm going to save my creative juice on something better. I would do nonagons next, but that's a lot of names, and you can just imagine what it would be as nonagons just have double triangular symmetry. Lets jump to 3D instead.

3D

So far I've been ignoring the up/down axis, but it exists. Let's look at some simple 3D shape systems!

Tetrahedral Directions

Now this is where things get interesting. There's lots of ways to orient our tetrahedron, but the way that makes the most sense is with one vertex facing forward, and one vertex that doesn't point left or right at all. This would be a very interesting system, as there's no up direction. There's a direction that points mostly up, but also a little bit backward. Also, the other two directions point mostly left and right, but also a little bit backward and down. Very stupid.

I haven't named any of these because I don't like the tetrahedral directions that much and I'm getting lazy. Coming up with random names takes a surprising amount of effort. (at least for me)

Icosahedral Directions

It's important to mention that I rotated the second icosahedron slightly, and that's why the forward and backward vertices are misaligned. Anyway, this system has a front and back. Then it has 5 directions that all point a little forward, and 5 directions that point a little backward. I've spun it around the forward/backward axis so that one pentagon vertex points straight up, and the other straight down. (Well, not straight up or down, there's still that little bit of forward and backward I mentioned. There's just no left/right.)

The reason I drew the front facing version like that is that anyone crazy enough to use this sytem probably has triangularly arranged eyes.

Dodecahedral Directions

This is the most complex directional system on this list, and that's why I put it last. There are a total of 20 directions. Like the icosahedral directions, this system has a perfect forward and backward. Then it gets really complex.

Conclusion

There's lots more I could do, like looking at irregular solids, designing systems for 4 dimensions, trying out more rotations, etc. But I'll leave that to you. This webpage isn't over yet though, I want to design one actually good system.

In order to improve upon our current system, we need to find flaws. The biggest flaw with our current system is that it's impossible to describe 120 degree and 72 degree angles. (Thirds and fifths) Pentagonal angles (while cool and pretty) aren't really that important, since pentagons can't tile, but hexagons can tile. So if you ever find yourself on the edges of a hexagonal tiling, you could say that you turn left and right at each intersection, but that's boring and wrong by 30 degrees.

Let's use a dodecagon to fix this! I did not put much effort into these names, all that matters is the shape.

You only need to learn 8 new words! Kesh and Pesh are the most important though, so you only really need to learn two. Well, in reality none of these are important, unless you live in a place with hexagonal city design.

In conclusion, pentagons are pretty, triangle tilings are cool, and octahedrons are the best shape to use for describing directions, in almost all situations.