Atomic Packing Factor of Simple Hexagonal Unit Cell

[forstajh]

How would I go about finding the APF for a simple hexagonal unit cell. Which is a rectangle. I know one length is a0(HCP) but I cannot figure out the other side of the rectangle. Also, wouldn't the height be the c?

[Gokul43201]

Okay, there's a few things to keep in mind here :

1. The unit cell is a right prism, the top and bottom faces being rhombuses (of 60 and 120 deg)

2. Besides the corner atoms of this unit cell, there's also an inside atom completely enclosed inside the prism

3. For a simple close-packed hexagonal unit cell, the value of c/a = SQRT(8/3). (This can be proved, if you wish, or used as it is.)

If you're not sure what the unit cell looks like, google it, to find a picture. If you do the calculation with the wrong picture in your head, you'll waste a bunch of time, so make sure you know what the unit cell looks like.