  We investigate quartification models in five dimensions, with the fifth
dimension forming an $S^1/Z_2\times Z_2'$ orbifold. The orbifold construction
is combined with a boundary Higgs sector to break the quartified gauge group
directly to a group $H\subset SU(3)^4$ which is operative at the electroweak
scale. We consider $H=G_{SM}\otimes SU(2)_\ell$ and $H=G_{SM}$, where $G_{SM}$
is the standard model gauge group, and find that unification occurs only when
the remnant leptonic colour symmetry $SU(2)_\ell$ remains unbroken.
Furthermore, the demands of a realistic low energy fermion spectrum specify a
unique symmetry breaking route for the unifying case of $H=G_{SM}\otimes
SU(2)_\ell$. We contrast this with four dimensional quartification models where
unification may be achieved via a number of different symmetry breaking routes
both with and without the remnant $SU(2)_\ell$ symmetry. The boundary Higgs
sector of our model may be decoupled to achieve a Higgsless limit and we show
that the electroweak Higgs doublet may be identified as the fifth component of
a higher dimensional gauge field.
