  A simple geometric algebra is shown to contain automatically the leptons and
quarks of a family of the Standard Model, and the electroweak and color gauge
symmetries, without predicting extra particles and symmetries. The algebra is
already naturally present in the Standard Model, in two instances of the
Clifford algebra $\mathbb{C}\ell_6$, one being algebraically generated by the
Dirac algebra and the weak symmetry generators, and the other by a complex
three-dimensional representation of the color symmetry, which generates a Witt
decomposition which leads to the decomposition of the algebra into ideals
representing leptons and quarks. The two instances being isomorphic, the
minimal approach is to identify them, resulting in the model proposed here. The
Dirac and Lorentz algebras appear naturally as subalgebras acting on the ideals
representing leptons and quarks. The resulting representations on the ideals
are invariant to the electromagnetic and color symmetries, which are generated
by the bivectors of the algebra. The electroweak symmetry is also present, and
it is already broken by the geometry of the algebra. The model predicts a bare
Weinberg angle $\theta_W$ given by $\sin^2\theta_W=0.25$. The model shares
common ideas with previously known models, particularly with Chisholm and
Farwell, 1996, Trayling and Baylis, 2004, and Furey, 2016.
