  A geometric approach to the standard model in terms of the Clifford algebra
$% C\ell_{7}$ is advanced. The gauge symmetries and charge assignments of the
fundamental fermions are seen to arise from a simple geometric model involving
extra space-like dimensions. The bare coupling constants are found to obey
$g_{s}/g=1$ and $g^{\prime}/g=\sqrt{3/5}$, consistent with SU(5) grand
unification but without invoking the notion of master groups. In constructing
the Lagrangian density terms, it is found that the Higgs isodoublet field
emerges in a natural manner. A matrix representation of $% C\ell_{7}$ is
included as a computational aid.
