Supersolid phases are quantum-entangled states of matter exhibiting the dual characteristics of superfluidity and solidity. Theory predicts that hard-core bosons on a triangular lattice can form such phases at half filling and near complete filling. Leveraging an exact mapping between bosons and spin- \(\frac{1}{2}\) degrees of freedom, here we show that these phases are realized in the triangular-lattice antiferromagnet K2Co(SeO3)2. At zero field, neutron diffraction reveals the development of quasi-two-dimensional \(\sqrt{3}\times \sqrt{3}\) magnetic order with Z3 translational symmetry breaking (solidity), though with reduced amplitude indicating strong quantum fluctuations. These fluctuations manifest as equidistant bands of continuum neutron scattering, where the lowest-energy mode is gapless at K \((\frac{1}{3}\frac{1}{3})\) , consistent with broken U(1) spin rotational symmetry (superfluidity). For c-axis-oriented magnetic fields near saturation, we find a second phase consistent with a high-field supersolid. These two supersolids are separated by a pronounced 1/3 magnetization plateau phase that supports coherent spin waves, from which we determine the underlying spin Hamiltonian.
