What is this type of paddle strop called, and how do you store/place it?

I'm wondering what kind of paddle strop this is below. I like how it looks... it's shaped like a belt grinder, or the belts in a car engine. I'm also wondering how one would store it or even place it on the table/counter-top, so as to not contaminate the surface on either side. Would one simply place some clean linens underneath, or simply make sure that the contacting counter-top surface is clean?

Thanks in advance!

What is this type of paddle strop called, and how do you store/place it?