We show how the grand unified theory based on the proof of the four color theorem can be obtained entirely in terms of the Poincare group of isometries of space and time. Electric and gauge charges of all the particles of the standard model can now be interpreted as elements of the Poincare group. We define the space and time chiralities of all spin 1/2 fermions in agreement with Dirac's relativistic wave equation. All the particles of the standard model now correspond to irreducible representations of the Poincare group according to Wigner's classification. Finally, we construct the Steiner system of fermions and show how the Mathieu group acts as the group of symmetries of the fundamental building blocks of matter."