Refining of triangular meshes and creation of a fractal mesh
 

Hi!
I am a new user of OpenFOAM. I have two questions.

1. I am working on a 2d geometry and I have used the command refineMesh -overwrite to refine a rectangular/quadrilaterial mesh. But when I try to refine a triangular mesh using the same command, it does not work. So is it possible to refine a triangular mesh?

2. I want to create a mesh for the following structure. It is a structure whose cross-section is a square Sierpinski fractal carpet and projected in the third dimension. Note this is not a menger sponge. Please see this picture carefully

https://postimg.org/image/z373pjbo9/

Any help will be highly appreciated.