There's a stone on the UK ebay at the moment, which is described as a coticule, but doesn't look like any of the other photos of cotis I've seen:

RARE VINTAGE COTICULE STRAIGHT RAZOR SHARPENING STONE IN WOOD BOX | eBay

It isn't worked or backed with another type of rock, it's quite natural looking.

I'm not going to bid on it, I'm just asking out of idle curiosity. (I may get a coti eventually, but not for some time I think.)