At first sight, liquids appear to be entirely devoid of symmetry: unlike crystals, there is no unit cell, and hence the space group operations that “build up” the unit cell contents from the asymmetric unit, and the subsequent unit cell translations that generate the whole crystal, are both irrelevant to liquids. It is, however, both possible and illuminating to consider the atomic arrangements in both liquids and crystals in a parallel manner. Starting from the basic elementary unit—a soft sphere for simple crystals and liquids—both kinds of structure can be “built up” through local “sub-unit” aggregates (tetrahedra and octahedra), which are then arranged in face-sharing mode in larger “super-units”; these are then embedded in the rest of the assembly to fill space. In the crystal case, the build-up operations are clearly defined local symmetry operations, which are applied in a regular sequence, and the embedding process is automatically satisfied by the unit cell translation operations. For the liquid, the same basic tetrahedral and octahedral sub-units can be used; provided the metrical identity requirements are relaxed, these can be arranged to form a finite number of topologically distinct “super-units”. The subsequent embedding of these super-units—which appears only to be possible with the help of other “defect” polyhedra—follows local symmetry operation rules which are as yet unknown. Understanding these local build-up symmetry operations, and their non-regular rules of application, would constitute a large part of the statistical geometrical structural theory of liquids called for by Bernal thirty years ago.