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Polytees

What are Polytees?

Polytees are shapes made from T-pipes joined end-to-end (not at junctions) An analogy a mathematician I am working with, Pontus von Brömssen, is that these are like polyominoes, but instead of connecting squares, you connect squares with one chipped edge, and that chipped edge cannot be connected.

Enumeration

The sequence of free polytees goes: 1, 4, 15, 99, 630, 4599, 34099, 261603
See A390515 on the OEIS.

List of Polytees

Monotees

There is one free monotee.

Ditees

There are four free ditees. Colored by symmetry: light blue is one-axis, purple is rotational, black is asymmetrical.

Tritees

There are 15 free tritees. Colored by symmetry: light blue is one-axis, black is asymmetrical.

References

Polytees - Polypad
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