The birth of E8 out of the spinors of the icosahedron

摘要: E8 is prominent in mathematics and theoretical physics, generally viewed as an exceptional symmetry eight-dimensional (8D) space very different from the we inhabit; for instance, Lie group features heavily 10D superstring theory. Contrary to that point of view, here show root system can fact be constructed icosahedron alone thus purely terms 3D geometry. The 240 roots arise 8D Clifford algebra a double cover 120 elements icosahedral group, generated by H3. As by-product, restricting even products vectors (spinors) 4D subalgebra algebra, one each induces 4D, which turn out also exactly systems. spinorial view explains their existence well unusual automorphism groups. This approach allows construct all systems within geometry three dimensions, opens up novel interpretation these phenomena