Show that in a hexagonal close-packed structure, atomic packing factor is 0.74.

Question

(i) In an orthogonal crystal structure with lattice parameters $a \neq  b \neq c$, draw the direction.                                                                                                                                     [2 1 2 ].

(ii) Show that in a hexagonal close-packed structure, atomic packing factor is 0.74. Take dimension c = 1.633 a.