Ising models on a pyrochlore oxide lattice have become associated with spin ice materials and magnetic monopoles. Ever more often, effects connecting magnetic and elastic degrees of freedom are reported on these and other related frustrated materials. Here we extend a spin-ice Hamiltonian to include coupling between spins and the O−2 ions mediating superexchange; we call it the magnetoelastic spin ice model (MeSI). There has been a long search for a model in which monopoles would spontaneously become the building blocks of new ground-states: the MeSI Hamiltonian is such a model. In spite of its simplicity and classical approach, it describes the double-layered monopole crystal observed in Tb2Ti2O7. Additionally, the dipolar electric moment of single monopoles emerges as a probe for magnetism. As an example we show that some Coulomb phases could, in principle, be detected through pinch points associated with O−2-ion displacements.Instituto de Física de Líquidos y Sistemas Biológicos