I am trying to figure out how to achieve the following:

• Starting with this representation for particles

  proton = {2/3, 2/3, -1/3, h1}
  electron = {0, -2/3, -1/3, h2}
  antiproton = -proton*{1, 1, 1, -1}
  positron = -electron*{1, 1, 1, -1}
  

where the first three numbers correspond to the length of the parallelepiped along x,y and z. The fourth number h1 <<1, h2<1 and h1/h2 is
equal to the ratio between the proton and electron masses.

I would like to create a class (dilator class) capable of presenting a graphical representation containing four parallelepipeds (one over the other) where the elements follow the following sequence (proton -> positron -> antiproton -> electron -> proton....) for positive spin and (proton -> electron -> antiproton -> positron -> proton....).

The second and fourth members of the sequence are rotated 90 degrees. Rotation by 90 degrees along x mean that the x axis is swapped with the fourth axis - For example for the proton (2/3,2/3,-1/3,h1) ->(h2,-2/3,-1/3,0)->(-2/3,-2/3,+1/3,h1)->(h2,2/3,1/3,0). This shows that the intermediate state are invisible (h2 is very small, the total 3D volume is very small).

Later I would like to create another class that would provide representation of n dilators into a regular polygon, e.g. three dilators would be represented as three dilators (each one containing four parallelepipeds one over the other) around a 360 degree circle (120 degrees apart).

n=5 would result in a pentagon, where in each corner a dilator would arise (four parallelepipeds one over the other).

Negative charges would just have green color - positive charges would be red. The length of the parallelepiped would be equal to the absolute value of the corresponding number.

This is my initial challenge. I thought about doing it using classes but I would accept any help. I am very new to Mathematica so this is very challenging.

This is an alternative representation of particles as fourth dimensional local metric deformations (negative axis means stretch, positive means compression). Spin is represented as an actual rotation in a non-compact fourth dimensional manifold. The four phases correspond to the tunneling between stationary states of local metric deformation. There is a spin=1/2 relationship between tunneling and spinning such that the particles are always in phase when they get flush with the 3D Hypersurface where we live.