If in the previous scenario we look for bigger brothers of Tom and Jerry with index 1,

then we have a pleasant surprise – not only we get 3.1 and 2.6, but also .

For and we constructed mirrors

as where ,

and G is either 2 or 3.

Regularized I-series for 2.6 and 3.1 has the same coefficients ,

so their mirrors should be related to squares of mirrors for and .

Consider .

Obviously it has the same as its isogeneous

Newton polytope for this kind of Laurent polynomials have number 432464 in grdb.

We can check that

has period sequence 11 and is mirror to 2.6,

has period sequence 22 and is mirror to 3.1.

But we can have even more – I find it very amusing that

has period sequence 7 and is mirror to .

Since singular toric variety in question is again a cone over surface, probably it won’t be hard to prove the existence of degenerations.

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