The crystal structure of vanthoffite {hexasodium magnesium tetrakis-[sulfate(VI)]}, Na₆Mg(SO₄)₄, was solved in the year 1964 on a synthetic sample [Fischer & Hellner (1964). Acta Cryst. 17, 1613]. Here we report a redetermination of its crystal structure on a mineral sample with improved precision. It was refined in the space group P2₁/c from a crystal originating from Surtsey, Iceland. The unique Mg (site symmetry 1) and the two S atoms are in usual, only slightly distorted octahedral and tetrahedral coordinations, respectively. The three independent Na atoms are in a distorted octahedral coordination (1×) and distorted 7-coordinations intermediate between a ‘split octahedron’ and a pentagonal bipyramid (2×). [MgO₆] coordination polyhedra interchange with one half of the sulfate tetrahedra in <011> chains forming a (100) meshed layer, with dimers formed by edge-sharing [NaO₇] polyhedra filling the interchain spaces. The other [NaO₇] polyhedra are organized in a parallel layer formed by [010] and [001] chains united through edge sharing and bonds to the remaining half of sulfate groups and to [NaO₆] octahedra. The two types of layers interconnect through tight bonding, which explains the lack of morphological characteristics typical of layered structures.