  We investigate bond percolation on the iterated barycentric subdivision of a
triangle, the hexacarpet, and the non-p.c.f. Sierpinski gasket. With the use of
the diamond fractal, we are able to bound the critical probability of
percolation on the non-p.c.f. gasket and the iterated barycentric subdivision
of a triangle from above by 0.282. We then show how both the gasket and
hexacarpet fractals are related via the iterated barycentric subdivisions of a
triangle: the two spaces exhibit duality properties although they are not
themselves dual graphs. Finally we show the existence of a non-trivial phase
transition on all three graphs.
