For routers the same hardware as in CalcHack will be used, optionally a better antenna.
Even though it isn`t a mesh network every CalcHack client can be set up as a basic router allowing clients in a radius of at about 200 meters to connect to it and send data peer to peer.
For accessing online resources (downloading apps, maybe even a wikipedia parser) there will be a Lan to CalcHack bridge needed, which for example could consist of a RPi connected to the router (CalcHack PCB) through the extension port. The RPi then preprocesses the data to make it easier to transfer and parse within the CalcHack network. For example a wikipedia article gets broken down into plain text and bitmaps.
Of course direct P2P transmissions are also possible, to say establish a single voice or video link between two calculators (think teacher to student screencapture, or a little help during difficult to communicate situations...) without blocking all the routers bandwidth.