There is no one "internet" per se...
its piles and piles of privately and publically peered networks.
The people "own" the routers (likely they are leased anyways form cisco, juniper, big iron etc

) are the specifc telecommuniatiosn company.
There are a FEW absolute true teir1 backbones sucha as UUNet, MCI, Level3 (RIP: Genuity/BBN) Sprint etc... and many many smaller players to say the least.
IF you want to see pictures just do itnernet searches for images. Cisco 12000's and the like.
They are nothing special to look at. Just large grey boxes with a few lights and ports on them.