I do not remember now where to find a suitable figure, but these are the coordinates of the corners of the 2 cubes:
neutrino & antineutrino: (0,0,0)
electron: (-1,-1,-1)
positron: (1,1,1)
down quarks: (-1,0,0), (0,-1,0), (0,0,-1)
down antiquarks: (1,0,0), (0,1,0), (0,0,1)
up quarks: (1,1,0), (1,0,1), (0,1,1)
up antiquarks: (-1,-1,0), (-1,0,-1), (0,-1,-1)
The particle-antiparticle pairs have an inversion symmetry over the origin.
The quark triplets have a rotational symmetry of order 3 around the principal diagonal of the cubes that passes through the origin.
The weak isospin and the hypercharge are an alternative equivalent expression of the charges, but I prefer this picture as it is easier to understand and visualize. It also demonstrates the quantized nature of the charges that determine the strong and electromagnetic interactions, and that they are based on the same quantum, so they are not independent interactions. The also quantized spin must be added as a fourth value, to completely determine the weak interactions too.
The various sets of values that can be taken as charges are related by bijections (one-to-one correspondences), so which are taken as fundamental is a matter of convention.
In any case the chromodynamics is useful only for providing qualitative insights and for distinguishing things that are possible from those that are impossible. It is completely useless for computing quantities that are useful in practice.
As it is also obvious in the parent article, it is still impossible to compute the mass and the magnetic moment of the proton, much less for any more complex nuclei or hadrons.
I do not remember now where to find a suitable figure, but these are the coordinates of the corners of the 2 cubes:
neutrino & antineutrino: (0,0,0)
electron: (-1,-1,-1)
positron: (1,1,1)
down quarks: (-1,0,0), (0,-1,0), (0,0,-1)
down antiquarks: (1,0,0), (0,1,0), (0,0,1)
up quarks: (1,1,0), (1,0,1), (0,1,1)
up antiquarks: (-1,-1,0), (-1,0,-1), (0,-1,-1)
The particle-antiparticle pairs have an inversion symmetry over the origin.
The quark triplets have a rotational symmetry of order 3 around the principal diagonal of the cubes that passes through the origin.
The weak isospin and the hypercharge are an alternative equivalent expression of the charges, but I prefer this picture as it is easier to understand and visualize. It also demonstrates the quantized nature of the charges that determine the strong and electromagnetic interactions, and that they are based on the same quantum, so they are not independent interactions. The also quantized spin must be added as a fourth value, to completely determine the weak interactions too.
The various sets of values that can be taken as charges are related by bijections (one-to-one correspondences), so which are taken as fundamental is a matter of convention.
In any case the chromodynamics is useful only for providing qualitative insights and for distinguishing things that are possible from those that are impossible. It is completely useless for computing quantities that are useful in practice.
As it is also obvious in the parent article, it is still impossible to compute the mass and the magnetic moment of the proton, much less for any more complex nuclei or hadrons.