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Water in polycrystalline ice at its melting point forms a system of veins at the three-grain junctions. The veins join together at nodes, which are the four-grain junctions. The shape of a node, a tetrahedron with non-spherical faces and open corners, is determined completely by the dihedral angle for water in contact with a grain boundary. Using the observed value for this angle, namely 33.6°, the paper computes the tetrahedral shape. This is a surface-tension problem with initially unknowndoi:10.3189/002214389793701437 fatcat:zs56kcmbzbb4pcy5funjc6fzea