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We have studied the magnetostructural phase diagram of multiferroic TbMn2O5 as a function of temperature and magnetic field by neutron diffraction. Dielectric and magnetic anomalies are found to be associated with steps in the magnetic propagation vector, including a rare example of a commensurate-incommensurate transition on cooling below 24 K, and in the structural parameters. The geometrically frustrated magnetic structure is stabilized by "canted antiferroelectric" displacements of the Mn3+ ions, an example of the magnetic Jahn-Teller effect. The Tb moments order ferromagnetically at low temperatures in an applied field, while the Mn magnetic structure is largely unchanged.