Building the unit cell…
Textbooks draw a cube and shade a quarter-circle in each corner. That drawing is a 2D cut. The packing fraction, however, is a 3D statement: how much of the cell is atom, and how much is empty. Clip the spheres at the faces, and the fractions become obvious — an eighth at each corner, a half on each face.
Four cells worth knowing
FCC and HCP both fill 74% of space (π√2 / 6) with twelve neighbors. The difference is stacking: ABCABC versus ABAB. BCC is more open, 68% (π√3 / 8), with eight neighbors. Alkali metals and α-iron use it. Diamond cubic is not a close packing at all. Carbon, silicon, and germanium sit in a tetrahedral network that fills only 34% (π√3 / 16). That is a crystal, not a pile of cannonballs.
Hard-sphere mode sizes each atom to the touching radius for that cell. Ball-and-stick then shrinks the spheres so you can see the bonds. Explode pulls sites off the center. Packed, clipping stays on so you can still count shared atoms.
What this is not
Real metals have thermal vibration, defects, and allotropes that swap structure with temperature. Iron, for example, is BCC, then FCC, then BCC again before it melts. This page is the unit cell, not a phase diagram. For a kinetic cartoon of melting and boiling, see the temperature simulator.
Questions the cell answers
Why do corner atoms look like orange slices?
Clipping planes cut the spheres at the unit-cell faces. A corner atom is shared by eight cells, so this cell owns one eighth of it. Six face atoms are each half-owned. Add them up, and FCC has four atoms per cell, BCC two, and diamond eight.
What does the explode slider do?
It pushes every site away from the cell center so you can count them. Packed, clipping cuts corners into eighths and faces into halves. Pulled apart, however, the clip planes switch off so you see whole spheres.
Is HCP denser than FCC?
No. Both fill 74% of space with coordination 12. They differ in stacking (ABC vs ABA), not in packing fraction. BCC is more open (68%). Diamond, however, is a tetrahedral network (34%) — a crystal, not a close packing.