Ah. Apologies for the over explain/mini-rant.
I'm not sure about formula, but if you find the equivalent photoshop RGB points you can see how its space differs. Colorspace is very much like regular 3d space and a rotation like this just needs a matrix to multiply the assorted colors through to get the new colors. So there is a matrix which will create the effect you're seeing, but in my experience matrix math isn't really something one does in their heads on the fly.
This particular colorspace is derived from a sort of "normal" RGB space that rotates around white, however its coordinates have been skewed. I don't remember quite enough matrix construction math to provide a sort of formulaic converter here right this minute, but yes its mathematically possible.
However, here's a sort of dirty version of the same conversion via illustrator and a distortion.
Basically there are more degrees of rotation in the skewed model between red and green than there are between green and blue. Its actually skewting the coordinate space making fewer possible cyan and magenta hues available, while adding many orange and chartreuse ones. The progression between colors in my little distorted circle there isn't exactly accurate to the wheel you linked, as it doesn't match the magenta range of the linked wheel.
The color offsets in degrees between cardinal 100% points on that wheel are (clockwise from top) 90 (yellow), 90 (green), 30 (cyan), 45 (blue), 60 (magenta), 45 (red)
A standard wheel would have 60 degree progressions between each point.