Probably not a useful new concept

Some time ago Nic and I were playing Zendo with MVK as master. It was clear that the rule had to do with orientation and color but we couldn't quite get it.

Nic had an insight: "All pieces of the same orientation (flat, upright, weird) must be the same color," he guessed.

This wasn't right, but it seemed we were pretty close. The same thing, except the distinction was two-way -- upright vs. non-upright? Or flat vs. non-flat? No, groundedness has to do with it too. Perhaps the categories are ungrounded, grounded flat, and grounded upright? (With grounded weird not mattering at all.)

It was clear that the rule had this form, but after more and more counterexamples and more and more ad-hoc dividing the ways the pieces could be grounded and oriented, MVK decided to just tell us: It was that any two pieces that were touching the ground with the same parts had to have the same color. That is to say, if we explicitly enumerate the classes this creates, we get

1. grounded upright;
2. grounded flat;
3. grounded weird, balanced on a base edge;
4. grounded weird, balanced on a long edge;
5. grounded weird, balanced on a base vertex;
6. grounded weird, balanced on its point;
7. ungrounded.

So, y'know, if a master in a game of Zendo ever pulls that on you, now you have the concept available.

-Harry