  We analyze a gauge-Higgs unification model which is based on a gauge theory
defined on a six-dimensional spacetime with an $S^2$ extra-space. We impose a
symmetry condition for a gauge field and non-trivial boundary conditions of the
$S^2$. We provide the scheme for constructing a four-dimensional theory from
the six-dimensional gauge theory under these conditions. We then construct a
concrete model based on an SO(12) gauge theory with fermions which lie in a 32
representation of SO(12), under the scheme. This model leads to a
Standard-Model(-like) gauge theory which has gauge symmetry SU(3) $\times$
SU(2)$_L$ $\times$ U(1)$_Y$($\times$ U(1)$^2$) and one generation of SM
fermions, in four-dimensions. The Higgs sector of the model is also analyzed,
and it is shown that the electroweak symmetry breaking and the prediction of
W-boson and Higgs-boson masses are obtained.
