Virtual spatial vectors in electrical engineering

I keep wondering whether the 3 vetors(R,Y,B) spaced 120 electrical degrees apart that we write on a sheet of paper- are in a plain?- say x plain. So we call them Rx, Yx, Zx

Can we have similar 3 phase vetors in say Y plain and 3 more in Z plain? Now we will have additionally Ry, Yy, By and Rz, Yz, Bz. Then what will be the electrical/ mathematical relation/ vector transformation relation between these vectors?

If this is practically possible, we can use it in transmitting signals with 3 times capacity per channel. Many more applications can be found. I have written a lengthy paper, but unable to attach it here. I got bogged down in mathematics, and in actual practical construction.
Can I get any help?

The material in this press release comes from the originating research organization. Content may be edited for style and length. Want more? Sign up for our daily email.