I first came across this 7-sided polygon here… http://isohedral.ca/heesch-numbers-part-3-bamboo-shoots-and-ice-cream-cones/

Eight of these fit into an 18-gon (octadecagon).

I replaced the two heptagons in the centre (and any space left over) with six ‘thorns’ (below).

There are now known to be 34 different arrangements of 6 ‘Bamboo Shoots’ and 6 ‘Thorns’ inside an 18-gon. There are an additional 26 if the mirror images of those arrangements without mirror symmetry are included, making a grand total of 60 (that’s ten more than I found)! The arrangements with grey colouring have mirror symmetry. Thank you to Michael Dowle for supplying this updated information and new diagram. The colours really help in understanding the method he used.

It seems that there are only three ways to tile the plane with the bamboo shoot and thorn, all creating ‘pulse’ tilings. The second example is a mirror of the first. Curiously though, mirroring the third is a duplicate of itself!?

You are welcome to correct me on any errors.