Please look at the problem here. What is the shape of the polygon at the end?
Start with an equilateral triangle with unit area. Trisect each of the sides and then cut-off the corners. In this case, we get a regular hexagon - see the picture below. Next, trisect each of the sides of the hexagon and cut-off the corners. This will give a dodecagon, but not a regular one.
Continue this process ad infinitum.
What is the SHAPE of the limiting "polygon"?
Not sure but I don't think it's going to be a circle