Background: A finite projective plane has point-line duality, and affine planes lack it. You can get a projective plane by adding a "line at infinity," and this is reversible.

Years ago I stumbled across this in constructing a counterexample to a graph conjecture, and I never found out if it was something people had realized or used before:

We can also recover point-line duality from an affine plane by just deleting one of the parallel classes of lines. <cont...>

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Anyone hear of this before, or can find something about it? It seemed kinda cool at the time, and I like this axiomatization.

I did see your post (in fact that's what reminded me of this), but hadn't gotten around to commenting. But Dobble/Spot-It is a projective plane (less two lines, conjecturally because of printing convenience); in my structure, there would be cards that shared no images, and more images that don't appear together on a card.

@bmreiniger sorry, misread your post!

Christian Lawson-Perfect@christianp@mathstodon.xyz@bmreiniger

You'll like this puzzle that I made recently: https://www.thingiverse.com/thing:3856293

That axiomatization is an encapsulation of why the game Dobble (Spot-It in the USA) works.