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I’ll add some words: it’s impossible to make the one with four colours symmetric.

…in a plane? Looks like power sets and hypercubes, so the n-th one can be projected symmetrically into (n-1)-space.

It’s interesting that some people looked at this and saw cubes in various dimensions. My first impression was a tree with each branch asking, “Which color should I eliminate?”

Great observations so far! Anyone, please feel free to add more observations, no matter how small.

1 (omitted—it would be an empty box, I suppose)

1 1

1 2 1

1 3 3 1

1 4 6 4 1

Combinations and binomial coefficients spring to mind.

Looks pretty neat!

Made with diagrams (http://byorgey.wordpress.com/2011/05/17/announcing-diagrams-preview-release/)?

Yes! You can find the code used to produce this diagram here:

http://patch-tag.com/r/byorgey/diagrams-cairo/snapshot/current/content/pretty/example/Hasse.hs

Awesome! I really like diagrams, not only because I was searching a way to build nice drawings, but also because it is a nice piece of code to learn how to make a DSL in Haskell. Thank you and all the contributors!

Cool, glad you like it! Let me know if you have any questions.

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