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This slide shows the motivation of the talk.

That is, as shown in the middle figure, one could specify any affine …

As a result, we could describe “fusion and fission” of …


Shown on the left is the standard” lattice which is generated by (1, 0, 0), (0, 1, 0), and (0, 0, 1).
And we have used the lattice to define flow of triangles in the previous slide.

On the other hand, as shown on the right, the “conjugate” lattice is the lattice which is generated by (0, 1, 1), (1, 0, 1), and (1, 1, 0).

And, as shown in the middle figure, only the slant triangles which induce the closed trajectory on the hyperplane are just covered by “peaks and valleys” of the conjugate lattice which is colored blue.