The width of the waveguide in the two cases is not the same, which is why you are getting different results. This is easily seen by looking at the epsilon files side-by-side. (Use "mpb-data -m 3 -r -n32" to see a rectangular supercell).

See the attached images, which I obtained by running your triangular and rectangular lattice control files.

Steven

<<inline: tri.png>>

<<inline: rect.png>>

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