Aperiodic composite crystals present long-range order without translational symmetry. These materials may be described as the intersection in three dimensions of a crystal which is periodic in a higher-dimensional space. In such materials, symmetry breaking must be described as structural changes within these crystallographic superspaces. The increase in the number of superspace groups with the increase in the dimension of the superspace allows many more structural solutions. This is illustrated in n-nonadecane-urea, revealing a fifth higher-dimensional phase at low temperature.
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