Is there a way to extract the "major edges" of a geometry after Weaverbird Subdivision Process?

Hi all,

I am trying to extract the major edge of a mesh after it has been subdivided with any weaverbird method. Please see attached image for example. I want to be able to extract the major curves generated by the initial edges of the cube. Or even split the mesh this way. Is anything like this possible? Thank you very much in advance