At first glance at the drawing we might think that the tile from which Escher starts is one of the birds, repeating itself through translations, symmetries and rotations.
We can start by looking for the nodes where several tiles join together:
And we could think of a Heesch 22 type tile with two sides of type G formed by the same type of line but symmetrical, and two sides of type C with their respective 180º turns.
Like this:
But this is not the solution, because 180º symmetries put the birds upside down. And in Escher tessellation there are no upside down birds.
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We need to look at Escher's drawing again. It seems that the two birds are neither equal nor symmetrical to each other:
This is only possible if the two different birds are part of the same tile:
Now this tile is a hexagon containing two birds with three translations to tessellate. The Heesch TTTTTT type. (Heesch 2)
Now the result is similar to the original Escher drawing:
In 1938 Escher was experimenting with tiles with two figures inside.
The same birds appear developed and gradually correcting their differences in Escher's famous drawing: "Day and Night"
Day and night. M.C. Escher 1938
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(Graphics made with "Explore Tessellations" Android app:
https://play.google.com/store/apps/details?id=com.nummolt.heesch.escher.tiles.tessellations)
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