We compute the three-body structure of the lowest resonances of 12 Be considered as two neutrons around an inert 10 Be core. This is an extension of the bound-state calculations of 12 Be into the continuum spectrum. We investigate the lowest resonances of angular momenta and parities, 0 ± , 1 − , and 2 + . Surprisingly enough, they all are naturally occurring in the three-body model. We calculate bulk structure dominated by small-distance properties as well as decays determined by the asymptotic large-distance structure. Both 0 + and 2 + have two-body 10 Be-neutron d-wave structure, while 1 − has an even mixture of p and d waves. The corresponding relative neutron-neutron partial waves are distributed among s, p, and d waves. The branching ratios show different mixtures of one-neutron emission, three-body direct, and sequential decays. We argue for spin and parities 0 + , 1 − , and 2 + for the resonances at 0.89, 2.03, and 5.13, respectively. The computed structures are in agreement with existing reaction measurements.