$-$quartz is hexagonal with space group $P622($#$180),$ with $a=5\mathrm{.}01,c=5\mathrm{.}47.$ Si atoms

sit at $(0\mathrm{.}5,0\mathrm{.}5,0\mathrm{.}333333)$; the $O$ ions are at $(0\mathrm{.}197,0\mathrm{.}803,0\mathrm{.}8333).$ Several other $Si{O}_2$

polymorphs are known, including derivatives of the diamond and wurtzite structures.

a$.$ Plot a unit cell showing the Si$-$O bonds. Make sure you have looked at the structure

in both $001$ and $100$ projections.

b$.$ What are the coordinations of the $Si$ and $O?$

c$.$ Contrast the polyhedra corner, edge, and face sharing with that for corundum.

d$.$ In your structure, identify the $6_2$ screw axis that is characteristic of quartz.