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We have investigated twin boundaries in double-lattice hexagonal close-packed metallic materials, focusing on their atomic geometry. Combining accurate ab-initio methods and large-scale atomistic simulations we address the following two fundamental questions: (i) What are the possible intrinsic twin boundary structures in hcp crystals? (ii) Are these structures stable against small distortions? In order to help end a decade-long controversy over the experimental observations of the atomic structures of twin boundaries, we have determined the energetics, spectra, and transition mechanisms of the twin boundaries. Our results confirm that the mechanical stability controls structures which are observed.