We study (dual) Longo-Rehren subfactors $M\otimes M^{opp} \subset R$ arising
from various systems of endomorphisms of M obtained from alpha-induction for
some braided subfactor $N\subset M$. Our analysis provides useful tools to
determine the systems of R-R morphisms associated with such Longo-Rehren
subfactors, which constitute the ``quantum double'' systems in an appropriate
sense. The key to our analysis is that alpha-induction produces half-braidings
in the sense of Izumi, so that his general theory can be applied. Nevertheless,
alpha-induced systems are in general not braided, and thus our results allow to
compute the quantum doubles of (certain) systems without braiding. We
illustrate our general results by several examples, including the computation
of the quantum double systems for the asymptotic inclusion of the E_8 subfactor
as well as its three analogues arising from conformal inclusions of SU(3)_k.