Template:Atomic packing factor (hexagonal)/doc

Calculates the atomic packing factor for hexagonal.

a=b≠c

α=β=90 γ=120

First this template determines the atomic radius by choosing the lesser of:
 * 1) 0.5 *
 * 2) 0.5 * ( (1*/3)^2 + (2*/3)^2 + (/2)^2)^0.5

Then the atomic packing factor is easily calculated.
 * number of Lattice points per unit cell * volume of atom / volume of unit cell

=

0.5 * 1 * ((3)^0.5 / 3) =

Examples
=

=

=

=

=

Equilateral triangle
Wikipedia:
 * The altitude (height) from any side is $$h=\frac{\sqrt{3}}{2} a$$.
 * The height of the center from each side, or apothem, is  $$\frac{h}{3} $$
 * The height of the center from each corner is therefore $$2\frac{h}{3}$$ = $$\frac{\sqrt{3}}{3} a$$