Supramolecular soft crystals are periodic structures that are formed by the hierarchical assembly of complex constituents, and occur in a broad variety of 'soft-matter' systems(1). Such soft crystals exhibit many of the basic features (such as three-dimensional lattices and space groups) and properties (such as band structure and wave propagation) of their 'hard-matter' atomic solid counterparts, owing to the generic symmetry-based principles that underlie both(2,3). 'Mesoatomic' building blocks of soft-matter crystals consist of groups of molecules, whose sub-unit-cell configurations couple strongly to supra-unit-scale symmetry. As yet, high-fidelity experimental techniques for characterizing the detailed local structure of soft matter and, in particular, for quantifying the effects of multiscale reconfigurability are quite limited. Here, by applying slice-and-view microscopy to reconstruct the micrometre-scale domain morphology of a solution-cast block copolymer double gyroid over large specimen volumes, we unambiguously characterize its supra-unit and sub-unit cell morphology. Our multiscale analysis reveals a qualitative and underappreciated distinction between this double-gyroid soft crystal and hard crystals in terms of their structural relaxations in response to forces-namely a non-affine mode of sub-unit-cell symmetry breaking that is coherently maintained over large multicell dimensions. Subject to inevitable stresses during crystal growth, the relatively soft strut lengths and diameters of the double-gyroid network can easily accommodate deformation, while the angular geometry is stiff, maintaining local correlations even under strong symmetry-breaking distortions. These features contrast sharply with the rigid lengths and bendable angles of hard crystals.