Good reference, thanks! Let's not forget that the OP's problem is still theoretical.
Here is a default Matlab biplot of the original "RGB" data from post #1. The plane containing principle components 2 and 3 passes through the center of mass, and divides the data into groups of 5 and 6 points, as one might guess. This is an instructive example as one can easily see that the maximum variance lies approximately in the "RG" plane.
I'm betting that @J-M-L's suggestion would work well:
project the data onto the first principal component (the direction of maximum variance), a 1D representation is obtained and then a standard median can be computed.