  The mechanics of biological tissues mainly proceeds from the cell cortex
rheology. A direct, explicit link between cortex rheology and tissue rheology
remains lacking, yet would be instrumental in understanding how modulations of
cortical mechanics may impact tissue mechanical behaviour. Using an ordered
geometry built on 3D hexagonal, incompressible cells, we build a mapping
relating the cortical rheology to the monolayer tissue rheology. Our approach
shows that the tissue low frequency elastic modulus is proportional to the rest
tension of the cortex, as expected from the physics of liquid foams as well as
of tensegrity structures. A fractional visco-contractile cortex rheology is
predicted to yield a high-frequency fractional visco-elastic monolayer
rheology, where such a fractional behaviour has been recently observed
experimentally at each scale separately. In particular cases, the mapping may
be inverted, allowing to derive from a given tissue rheology the underlying
cortex rheology. Interestingly, applying the same approach to a 2D hexagonal
tiling fails, which suggests that the 2D character of planar cell cortex-based
models may be unsuitable to account for realistic monolayer rheologies. We
provide quantitative predictions, amenable to experimental tests through
standard perturbation assays of cortex constituents, and hope to foster new,
challenging mechanical experiments on cell monolayers.
