the crystalline state
Imagine an infinite sheet of wallpaper: the same motif stamped again and again at perfectly regular spacings, so that from any one stamp the whole pattern looks identical. A crystal is that idea carried into three dimensions, atoms arranged in a pattern that repeats periodically through space. The crystalline state is the condition of matter in which atoms sit on a regular, repeating grid. Most metals, table salt, quartz, and ice are crystalline.
Precisely, a crystal has long-range order: knowing where the atoms are in one small repeating block (the unit cell) lets you predict, exactly, where every atom sits even billions of cells away. That repeating block tiles all of space. The mathematics is clean and complete: there are exactly 7 crystal systems, 14 Bravais lattices, and 230 space groups, a finished enumeration of every way a pattern can repeat periodically in three dimensions, not a list still being added to.
Because the arrangement is periodic, a crystal produces sharp diffraction spots when hit with X-rays, the repeat acts like a grating, and this is how crystal structures are solved. Periodicity also gives crystals flat natural faces, definite melting points, and direction-dependent (anisotropic) properties. Honest reminder: the perfectly repeating crystal is an idealization, every real crystal contains defects (vacancies, dislocations, grain boundaries), and those imperfections are often exactly what makes it useful.
Table salt (NaCl) grows as tiny cubes. That cubic outward shape is a direct echo of the cubic, periodic way its sodium and chlorine atoms repeat inside.
Salt's cubic shape comes straight from the cubic periodicity of its atoms.
A material can be crystalline without looking like a gem. A steel paperclip is crystalline (made of millions of tiny crystals); the word refers to the periodic atomic arrangement, not to a transparent, faceted appearance.