  Motivated by orbifold grand unified theories, we construct a class of
three-family Pati-Salam models in a Z6 abelian symmetric orbifold with two
discrete Wilson lines. These models have marked differences from
previously-constructed three-family models in prime-order orbifolds. In the
limit where one of the six compactified dimensions (which lies in a Z2
sub-orbifold) is large compared to the string length scale, our models
reproduce the supersymmetry and gauge symmetry breaking pattern of 5d orbifold
grand unified theories on an S1/Z2 orbicircle. We find a horizontal 2+1
splitting in the chiral matter spectra -- 2 families of matter are localized on
the Z2 orbifold fixed points, and 1 family propagates in the 5d bulk -- and
identify them as the first-two and third families. Remarkably, the first two
families enjoy a non-abelian dihedral D4 family symmetry, due to the geometric
setup of the compactified space. In all our models there are always some color
triplets, i.e. (6,1,1) representations of the Pati-Salam group, survive
orbifold projections. They could be utilized to spontaneously break the
Pati-Salam symmetry to that of the Standard Model. One model, with a 5d E6
symmetry, may give rise to interesting low energy phenomenology. We study gauge
coupling unification, allowed Yukawa couplings and some of their
phenomenological consequences. The E6 model has a renormalizable Yukawa
coupling only for the third family. It predicts a gauge-Yukawa unification
relation at the 5d compactification scale, and is capable of generating
reasonable quark/lepton masses and mixings. Potential problems are also
addressed, they may point to the direction for refining our models.
