Yes vent holes cover the entire left and right sides, and even most of the top has it too. Before, I used a Ubee DVW326 modem and that had mounting holes on one side, and like the Arris TG2472 it is a vertical modem. I'd like to put this as high as possible, on the ceiling or close to it. Most shelves are short so would need a really tall one.
I was thinking more of a floating shelf. A floating shelf is basically a small board to mount on a wall. The natural springiness of a coax cable, however, would make it difficult to keep the modem in place on the shelf. To combat that, I'd use Velcro strips.
If you don't want to bother with mounting a shelf, you could try zip ties. I don't know what you used to mount your Ubee, but there are Stud-Mounted Cable Ties on the market. This is industrial hardware and usually sold in bulk.
If you want to go with cable ties, find a company on the Internet and explain your application in an email. I've found many company gracious to help me with a project.