What would you call the polymerised sheet-like polymer arising from Fittig reaction of 1,3,5-trichlorobenzene? If we dip a sample of chloroalkane in an ethereal solution, radicals form at the sites where chlorines are attached, which subsequently pair with other radicals.

Now, consider 1,3,5-trichlorobenzene:



If I attempted to perform a Wurtz-Fittig reaction with this, I suspect the product would be a two dimensional polymerised product. I drew a portion of it:



This polymer is quite interesting. Has this been observed before? Does it have a name?

While looking for the name of this molecule is my primary concern, it would be great if I could also get some information about its properties. This polymer looks like a "hollow" version of graphene, so I believe this would have some properties of graphene, although quite lighter. I think this could conduct electricity, due to conjugated $\pi$ systems of benzene rings. I also believe it would be quite porous, and probably allow small molecules like $\ce{H2O}$ to pass through.
Ignoring the complex challenges it would take to make such a structure, the name is rather unclever with the literature referring to it as "holey graphene". You could probably take this a step further with your hypothetical material and call it :


well-ordered holey graphene
or better yet, well-ordered monodisperse-C6-holey graphene.


with C6 alluding to the missing $\ce{C6}$ ring that would be present in perfect graphene. Materials science has very unrigid naming conventions. If you make it first, you can greatly influence the literature terms.

As far as conductivity goes, I agreed that it would likely be conductive or semi-conductive at a minimum similar to poly(9,10-anthracene diylidene).