Expanding on properties of polyhexes in images in the Wikipedia article: https://en.wikipedia.org/wiki/Polyhex_(mathematics)

Flat colors within a polyhex represent how many sides of the given hexagon connect to other hexagons within the polyhex (orange=1, blue=2, purple=3, red=4).

Faceted hex markers are colored by which category the adjacent polyhex belongs to.

• Pink are all similarly 1orange-{n:1-3}blue-1orange, like a two-headed worm.

• Grey are 1blue-2purple triads with 1orange ends on each of the purples.

• Turquoise are 2blue-1purple triads with a {n:0-1}blue+1orange tail on the purple.

• Green are (two 1orange "pigtails" or "mouse ears")-1purple-{n:0-1}blue-1orange.

• Lavender indicates no orange hexes within the polyhex.

Pentahexes:

The four Yellow pyramidal hex markers indicate unique pentahex configurations. Of these, three include a red hex, one has three purple hexes, and two have no orange hexes at all.