The role of the spatial organization of chromatin in gene regulation is a long-standing but still open question. Experimentally it has been shown that the genome is segmented into epigenomic chromatin domains that are organized into hierarchical sub-nuclear spatial compartments. However, whether this non-random spatial organization only reflects or indeed contributes-and how-to the regulation of genome function remains to be elucidated. To address this question, we recently proposed a quantitative description of the folding properties of the fly genome as a function of its epigenomic landscape using a polymer model with epigenomic-driven attractions. We propose in this article, to characterize more deeply the physical properties of the 3D epigenome folding. Using an efficient lattice version of the original block copolymer model, we study the structural and dynamical properties of chromatin and show that the size of epigenomic domains and asymmetries in sizes and in interaction strengths play a critical role in the chromatin organization. Finally, we discuss the biological implications of our findings. In particular, our predictions are quantitatively compatible with experimental data and suggest a different mean of self-interaction in euchromatin versus heterochromatin domains.