\({6\choose3}*{3\choose2}=60\)
or
\({6\choose2}*(6-2)=60\)
particles. Each of the six orthogonal dimensions has ten particles traveling along it at speed, \(v=c\). If every of these particles can be used to affect/access that dimension, then it would seem that each dimension has ten "shadow dimensions".
All such particles are however, equivalent along those dimensions. In the post "Lingpoche, 凌波车 II", the three waves were so chosen as the particles have zero space velocity, \(v=0\); none of the three space dimensions are part of their triplet, (\(t_g\), \(t_c\), \(t_T\)).
This is assuming that the three space dimensions are distinguishable.
In the case where the space dimensions are indistinguishable, there are,
\(1*3+({3\choose1}*2*2)+{3\choose2}*1*3+1*3=27\) particles.
In the first part, we construct a wave of three orthogonal space dimensions each existing in 3 time dimensions.
In the second part, we construct a wave of one time dimension and two space dimensions, for which there is three. Each of these three waves can exist in either of the two remaining time dimensions. We further differentiate those dimensions in the triplet that define the wave in oscillation and that for which it is at speed \(c\).
The third term is for a wave with one space dimension and two time dimensions. This wave exists in the remaining time dimension. And we differentiate the wave that oscillate between two time dimensions and has space speed \(c\) from the those oscillating between one time dimension and one space dimension. Together, for a given triplet, there can be three type of waves, because the component for which its speed is \(c\) is all different as the wave is rotated.
The last term is for waves of three time dimensions, from which we differentiate those time dimensions in oscillations and that along which the wave has speed \(c\). These waves have zero speed in space.
In this case, there are three distinguishable time dimensions and one space dimension of three aspects (or three space dimensions but indistinguishable). We are incapable of distinguishing the three space dimensions, just as the three time dimensions are not measured independently. But we do have charged particles that we attribute their charge property to their existence along the \(t_c\) time axis; mass that exist along the \(t_g\) time dimension and heat that exist along the \(t_T\) time dimension.
Otherwise mere science fiction.
