The study of self-assembly processes is of key importance for fundamental science and modern technologies. Cubic water clusters of D and S symmetry show great potential as building blocks for self-assembly. The objective of this paper is to construct possible ice structures formed by hydrogen bonding of these very stable water clusters. A number of such structures are herein presented, including quasi-2D and 3D ices as well as spatial layered and tubular ices. The energetics and structure of many configurations differing in the arrangement of hydrogen atoms in hydrogen bonds have been studied. It was established that the proton disorder of all such ices is of island type. The residual entropy of these ices is equal to ln(3)/4 in dimensionless form. For layered structures formed by the stacking of multiple bilayers, the determining role of the van der Waals interactions is shown. Note that, for all considered ices, the lowest-energy configurations are formed only by clusters of D symmetry.
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