  Self-consistent field theory (SCFT) has established that for cubic network
phases in diblock copolymer melts, the double-gyroid (DG) is thermodynamically
stable relative to the competitor double-diamond (DD) and double-primitive (DP)
phases, and exhibits a window of stability intermediate to the classical
lamellar and columnar phases. This competition is widely thought to be
controlled by "packing frustration" -- the incompatibility of uniformly filling
melts with a locally preferred chain packing motif. Here, we reassess the
thermodynamics of cubic network formation in strongly-segregated diblock melts,
based on a recently developed medial strong segregation theory ("mSST")
approach that directly connects the shape and thermodynamics of chain packing
environments to the medial geometry of tubular network surfaces. We first show
that medial packing significantly relaxes prior SST upper bounds on the free
energy of network phases, which we attribute to the spreading of terminal chain
ends within network nodal regions. Exploring geometric and thermodynamic
metrics of chain packing in network phases, we show that mSST reproduces
effects dependent on the elastic asymmetry of the blocks that are consistent
with SCFT at large $\chi N$. We then characterize geometric frustration in
terms of the spatially-variant distributions of local entropic and enthalpic
costs throughout the morphologies, extracted from mSST predictions. We find
that the DG morphology, due to its unique medial geometry in the nodal regions,
is stabilized by the incorporation of favorable, quasi-lamellar packing over
much of its morphology, motifs which are inaccessible to DD and DP morphologies
due to "interior corners" in their medial geometries. Finally, we use our
results to analyze "hot spots" of chain stretching and discuss implications for
network susceptibility to the uptake of guest molecules.
