It's dealer/region specific. Here, I've got the same fabric cover as Mendel but I also got the "old school" vinyl book-style cover that holds the manual on one side and the other thinner books on the other in the Toyota grey colour.
We got a real leather case with the Lexus, and faux leather case (actually fairly nice vinyl) for the Prius C. Even my DeLorean is a plastic flip case with a snap button...
The one I got is vinyl/plastic something, but it doesn't look seriously in need of ironing (like all my shirts these days), and they manage to give it a flocked, cloth-like texture. High highfalutin.
