This is the tenth installment of the Fortnightly Topic Challenges Rerun described here and the fifty-first installment of the FTCs overall, with topics suggested and voted on here. This fortnight's topic is "Non-rectangular grids" (suggested by Bubbler) and will span from the 7th of March to the 20th of March. During this period, we will compile the list of relevant questions and post it as an answer to this question.
In the meantime, please go and propose and vote on future challenges!
Everyone have fun, and happy puzzling!
Link to other Fortnightly Topic Challenges.
NOTE
The suggestion is copied to this post for posterity.
Non-rectangular grids
Create a puzzle that acts on any kind of non-rectangular grids. The grid can be simple triangular or hexagonal grids, but be creative: there are so many different plane tilings using regular polygons, and you can even use non-regular ones!
Excellent examples include Octagonal Kurotto and Karst - a variant of Cave. Cryptic hourglass is also a notable example of (essentially hexagonal) grid applied to a crossword in a non-traditional way (the words can bend in the middle).
Personally inspired by snub square tiling, whose dual circle packing has an interesting property that all circles touch with exactly five other circles:
