I have observed in the past when fiddling with gears that an axle "meshed" with a 12T gear, in the spot next to it, it is actually possible for the axle to function as a 4-tooth gear with the 12T gear, creating a 1:3 ratio in about the same space as a traditional 8:8 gear setup. Later, when I got my first 28T gears, I found that it can mesh with the axle as well. There may be some spacings in two "dimensions" that work with different gears, but I haven't really looked for them.

Of course, most of the time this is impractical, because there is unusually high friction between the axle and the gear, and under torque it will generally skip, but I suppose it might come in handy some day.

P.S. I would have put images on here of the concept, but it is a bit of a bother for me, and I suppose you can imagine it yourself.

I already uploaded this here.

Not a fan of this. Sure, it works but the gear is pushed outwards, so there is much stress here.

Yeah, it is pretty much useless in practice. I only posted it as a "fun fact" of sorts.

 

Theoretically, a 4 tooth gear would be the natural continuation of the double bevel gears, but a cross axle's 'teeth' don't have the right shape to mesh with other gears. 

Does that leave room for a new part that is half axle and half 4-tooth gear? Think of the possibilities of a 1 stud wide bevel gear...

The backlash on a 4-tooth gear would be pretty bad though.

43 minutes ago, lmdesigner42 said:

Does that leave room for a new part that is half axle and half 4-tooth gear? Think of the possibilities of a 1 stud wide bevel gear...

The backlash on a 4-tooth gear would be pretty bad though.

I think that there could be such a part, but it would have the downfall of having to be molded into an axle, since an axle couldn't fit inside of it. Thus, flexibility in attachment would be limited to whatever size axle Lego decided to put it on/in.