Crystal
A crystal is a solid whose atoms are arranged in a repeating three-dimensional pattern, producing flat faces and sharp angles.
Definition
A crystal is a solid whose tiny particles are lined up in a repeating pattern, like bricks in a wall, and that neat pattern is why crystals often have flat sides and sharp corners. More precisely, atoms, ions, or molecules occupy positions in an ordered lattice that repeats in three dimensions, and the lattice controls the crystal's outer shape (habit), its cleavage, and many optical properties. Crystals grow from cooling melts, evaporating solutions, or vapor. At the advanced level, a crystal is a solid with long-range translational order described by one of $14$ Bravais lattices and $32$ point groups, grouped into $6$ (or $7$) crystal systems. Growth requires nucleation followed by addition of atoms to the lattice, at a rate governed by supersaturation or undercooling, and X-ray diffraction reveals lattice spacing through Bragg's law, $n\lambda = 2d\sin\theta$.
Example
Grow sugar crystals on a string in a jar of sugar water; as the water evaporates, the sugar molecules stack into clear, blocky crystals. Halite forms cubes because sodium and chloride ions alternate in a cubic lattice, quartz forms six-sided prisms ending in points, and the emeralds mined near Hiddenite, North Carolina, are hexagonal crystals of the mineral beryl. In a granite pluton cooling over hundreds of thousands of years, quartz and feldspar reach centimeter size, while the same magma erupted as rhyolite lava quenches into microcrystalline groundmass or glass. Obsidian is an amorphous solid with no lattice at all.
Key Insight
Every snowflake is a crystal of ice, and its six arms come from the way water molecules lock together in a hexagonal pattern. Crystal size records cooling time: big crystals mean slow cooling underground, tiny crystals mean fast cooling at the surface. Polymorphs such as calcite and aragonite, both $CaCO_3$, show that the lattice rather than the formula defines the crystal. Which polymorph forms depends on temperature, pressure, and even the magnesium content of seawater.