  We study the recent construction of subfactors by Rehren which generalizes
the Longo-Rehren subfactors. We prove that if we apply this construction to a
non-degenerately braided subfactor N subset M and alpha-induction, then the
resulting subfactor is dual to the Longo-Rehren subfactor M tensor M^opp subset
R arising from the entire system of irreducible endomorphisms of M resulting
from alpha-induction. As a corollary, we solve a problem on existence of
braiding raised by Rehren negatively. Furthermore, we generalize our previous
study with Longo and Muger on multi-interval subfactors arising from a
completely rational conformal net of factors on S^1 to a net of subfactors and
show that the (generalized) Longo-Rehren subfactors and alpha-induction
naturally appear in this context.
