Cell decomposition of torus into seven polygons where each two share at least one side

Question

The four-color theorem of Appel and Haken says that any map in the plane can be colored with at most four distinct colors so that two regions which share a common boundary segment have distinct colors.

Question. Is there a cell decomposition of the torus into 7 polygons such that each two polygons share at least one side in common?

Answer 1

Yes. On A torus, $7$ is the maximum. See here: [https://en.wikipedia.org/wiki/Four_color_theorem#Generalizations]

Answer 2

You might want to have a look at this:

It is known that at most seven colours are required to colour any map on the torus, and this construction proves that it is the best possible bound.