Let denote the triangular lattice with wraparound. Call an orientation of an assignment of a direction to each edge of , and denote the number of orientations of such that each vertex has three inwardly directed and three outwardly directly edges by . Such an orientation is said to consist of Eulerian orientation.
Baxter showed that
(1)
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(2)
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(3)
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(OEIS A104956; Finch 2003, p. 412), which is known as the twenty-vertex entropy constant (a term coined here for the first time).