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We investigate bond percolation on the iterated barycentric subdivision of atriangle, the hexacarpet, and the non-p.c.f. Sierpinski gasket. With the use ofthe diamond fractal, we are able to bound the critical probability ofpercolation on the non-p.c.f. gasket and the iterated barycentric subdivisionof a triangle from above by 0.282. We then show how both the gasket andhexacarpet fractals are related via the iterated barycentric subdivisions of atriangle: the two spaces exhibit duality properties although they are notthemselves dual graphs. Finally we show the existence of a non-trivial phasetransition on all three graphs.

Bond percolation on a non-p.c.f. Sierpi\'nski Gasket, iterated barycentric subdivision of a triangle, and Hexacarpet