HCP unit cell c-axis Today I was asked to show that the perpendicular height, $H,$ of a regular tetrahedron is related to the length of a side, $L,$ of the tetrahedron, by $H = \sqrt{(2/3)} \cdot L$. I did this no problem.

I was then asked:
Explain how this is relevant in determining a relationship between the unit cell parameters, $a$ and $c$ of a hexagonal-close packed crystal structure: $c = 1.633 · a$.

Could anyone possibly help me out here?
A picture is worth a thousand words (see the two tetrahedra heights making up the vertical c-axis?):

The HCP packing has layers of closest-packed spheres in an ABAB... pattern. The distance between layers is one height of a tetrahedron, and you need two layers to get a repeating structure along c, i.e. the unit cell parameter.
(picture found at https://chemistry.stackexchange.com/a/111921)