= Solution
A <Bravais lattice> is a set of equivalent points generated by integer combinations of three independent translation vectors. A <crystal motif> is the arrangement of atoms attached identically to every <lattice point>. Together they specify the periodic <crystal structure>: lattice translations repeat the motif without changing its internal arrangement.
A <unit cell> is a region whose translations tile the structure. A <primitive unit cell> contains one <lattice point> after sharing boundary points with neighboring cells. A conventional cell can contain more than one <lattice point> to display the crystal's symmetry with simple axes and angles; for example, a conventional face-centered cube has four lattice points but a less visually symmetric primitive cell has one.
\b[Rotational symmetry compatible with a periodic three-dimensional lattice has order $1,2,3,4$ or $6$], as expressed by the <crystallographic restriction theorem>. A crystallographic fivefold axis is excluded from an ordinary periodic crystal. This statement concerns exact lattice symmetry; it does not exclude local fivefold atomic arrangements or nonperiodic ordered structures.
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