In $\mathrm{hcp}$ lattice, if a plane is drawn parallel to layers $\mathrm{A}$ and $\mathrm{B}$, at a distance $\frac{\mathrm{c}}{8}$ above the layer $\mathrm{B}$, it passes through centres of $\mathrm{x}$ tetrahedral and $\mathrm{y}$ octahedral voids. A plane parallel to layer $\mathrm{A}$, at a distance $\frac{\mathrm{c}}{8}$ just below it passes through centres of $\mathrm{p}$ tetrahedral and $\mathrm{q}$ octahedral voids. Find $\left(\mathrm{x}+\mathrm{y}+\mathrm{p}+\mathrm{q}\right)$. $\mathrm{c}$ is the cell parameter of hcp lattice, the vertical edge length.

A two dimensional solid is made by alternating circles with radius $\mathrm{a}$ and $\mathrm{b}$ such that the sides of the circles touch. The packing fraction is defined as the ratio of the area under the circles to the area under the rectangle with sides of length $\mathrm{x}$ and $\mathrm{y}.$

The ratio $\mathrm{r}=\mathrm{b}/\mathrm{a}$ for which the packing fraction is minimized is closest to:

What are the examples of hexagonal close-packed structure?

The pattern in Hexagonal close packing and cubic close packing are same. Is the statement true or false?