You can easily compile these standalone images with pdflatex, e.g.:
pdflatex example.tex
To produce a PNG image in linux, use ImageMagick's convert command, e.g.:
convert -density 400 -quality 90 example.pdf images/example.png
 |
|---|
| Honeycomb-Kagome lattice |
 |
|---|
| Honeycomb-Kagome unit cell |