  Chirality transfer from the level of molecular structure up to mesoscopic
lengthscales of supramolecular morphologies is a broad and persistent theme in
self-assembled soft materials, from biological to synthetic matter. Here, we
analyze the mechanism of chirality transfer in a prototypical self-assembly
system, block copolymers (BCPs), in particular, its impact on one of the most
complex and functionally vital phases: the cubic, triply-periodic, gyroid
network. Motivated by recent experimental studies, we consider a
self-consistent field model of ABC* triblock copolymers possessing an end-block
of chain chemistry and examine the interplay between chirality at the scale of
networks, in alternating double network phases, and the patterns of segmental
order within tubular network domains. We show that while segments in gyroids
exhibit twist in both polar and nematic segmental order parameters, the
magnitude of net nematic twist is generically much larger than polar twist, and
more surprising, {\it reverses handedness} relative to the sense of polar order
as well as the sense of dihedral twist of the network. Careful analysis of the
intra-domain nematic order reveals that this unique chirality transfer
mechanism relies on the strongly biaxial nature of segmental order in BCP
networks and relates the {\it biaxial twist} to complex patterns of frame
rotation of the principal directors in the intra-domain texture. Finally, we
show that this mechanism of twist reversal leads to chirality selection of
alternating gyroid networks in ABC* triblocks, in the limit of very weak
chirality .
