The best way to think about what crystals are like and why they have the properties they do, is to imagine them from the inside or, better still, to see them from the inside as you can in this installation.
The distribution of red and blue balls represents the structure of sodium chloride – that is, table salt. The red and blue balls correspond to chloride and sodium ions respectively, and they are distributed in a cubic structure in alternate rows (chloride-sodium-chloride…) perpendicular to each other.
If you observe the balls from any angle you will notice that there are red and blue balls in every part of the crystal and approximately in the same proportion whatever the volume you are looking at. The balls are homogeneously distributed. Looking more attentively, it is easy to appreciate that the geometric distribution of the balls creates rows (alignments of balls) and planes (two-dimensional surfaces) in defined directions, and that the sequence of balls is different in different directions.
For example, in this view of the crystal you can observe different ball alignments. See that some of them (marked as L1) are all the same colour, while others (like those marked L2) are alternating colours. The same thing happens with the planes. Can we see two-dimensional groupings of balls of just one colour and of alternating colours? This is a fundamental property of crystals: anisotropy. Imagine that if the crystal has physical properties (piezoelectricity, polarisation, electronic conduction…) that depend on the local order of the atoms, these properties will be anisotropic – in other words, they will occur in certain directions of the crystal and not in others. This anisotropy in the properties is what makes crystals so useful in technological applications.
Moving around the installation you can also observe the relation between the atomic structure and the global symmetry of the crystal. A crystal with a cubic structure like this one can have rotation symmetries 2, 3 and 4 as well as planes of symmetry. The figures below show the structure and the cube that all the balls form from determined directions that allow you to see symmetries 2, 3 and 4 of the atoms and of the crystal simultaneously.