For this kind of tiling, we begin with the obtuse triangle to the left as our fundamental domain. We then rotate about the blue/green vertex and reflect across the red edge.

To see the reflexive and 3-fold symmetry of this tiling, imaging rotating the entire tiling about one of these blue/green vertices. The the rotated tiling matches the original perfectly, as if we had never rotated the tiling. The same thing happens when we reflect the tiling across any of the red lines of relfection.

Using the p3m1 symmetry group, we can construct the hexagon to the right from our original tile from above. You can recreate the whole tiling by translating around the hexagon, which means p3m1 tilings are periodic, like all wallpaper tilings.

Kali denotes this symmetry by "*333". You can go to now to experiment with symmetry p3m1.