Abstract
It has recently been recognized by the author that the quantum contextuality paradigm may be formulated in terms of the properties of some subgroups of the two-letter free group G and their corresponding point-line incidence geometry G. I introduce a fundamental homomorphism f mapping the (infinitely many) words of G to the permutations ruling the symmetries of G. The substructure of f is revealing the essence of geometric contextuality in a straightforward way.