Group theory is a good way to study Particle Physics, when all the details are not known. U(1) x SU(2) x SU(3) is a good example as the symmetry group of the Standard Model (SM). It is well established, yet it is still a mystery why these symmetries, and why not a different or bigger group. The paper starts with an analysis of multi-fold aspects inspired from the Geometric Unity (GU). The first stages of the GU approach are contrasted with the multi-fold space time matter induction approach. It leads to different ways to characterize the symmetries of the 4D spacetime in the embedding space: Two unoriented 7D space time, tagged to cover a left and a right chirality, undefined in 7D, and therefore a Spin(7,7) symmetry. Spin (7,7) can be reduced by symmetry breaking to Sl(2,ℂ) x U(1) x SU(2) x SU(3), via a whole bunch of different paths and possible interim symmetries. The first term corresponds to General Relativity (GR) in 4D with Lorentz symmetries, while the rest are the SM symmetries associated to Quantum Physics. This 7D space, with chiral labels, is a local 7D ε neighborhood seen from the 4D spacetime, through multi-fold entry, exit or mapping points, locally embedding it, without Physics in it and implementing space time matter induction and scattering in the 4D multi-fold spacetime, ensuring U(1) x SU(2) x SU(3) for the SM, and induction of the SM particles. Indeed, the doubling of the spacetime sharing time as 7D embedding space explains the algebra doubling on non-commutative geometry in 4D that also predicts the SM particles. Revisiting the multi-fold mechanisms, we explicitly detail why a multi-fold spacetime carries U(1) x SU(2) x SU(3) symmetries, in addition to Lorentz symmetry. Also, GR reigns in the embedding space, Ricci flat or Einsteinian. It allows us to revisit aspects of wormhole traversability.Explaining why SM has the symmetry that it has is quite unique. So far, the GUTs failures to provide such an explanation, made U(1) x SU(2) x SU(3) even more puzzling. Furthermore, supersymmetry is not physical/A consequence of this paper is that GR, or the Hilbert Einstein action contains fully the Standard, and that there is no need to invoke fine-tuning or multiverses to explain our universe.