For several types of polycrystalline ice of different origins, the spatial lattice orientation of each crystal was determined by measurements of both the a- and c-axis orientations. Analyses of the orientations of adjoining crystals showed that a great majority of adjoining crystals may be in a twinning relation. With special reference to the multi-maximum c-axis preferred-orientation fabric (the so-called “diamond pattern”), which is expected to occupy the largest part of a glacier ice mass, the crystal boundary structure was estimated. The preferred c-axis orientations of this fabric were explained as being the result of coincident oxygen-oxygen lines (hydrogen-bond lines) between adjoining crystals being concentrated in the orientations where seven oxygen-oxygen lines of one single crystal of ice are distributed. From the above result, it was concluded that the multi-maximum fabric is of the polycrystalline structure closest to the structure of a single crystal of ice among all the fabrics found in large ice masses. It is found that the occurrence, in glaciers and ice sheets, of a multi-maximum fabric has a bias to the parts which have undergone a strong shear deformation for a long time. It is thus suggested that plastic deformation of ice with this fabric may be attributed to mechanical twinning due to a strong shear stress.