Pigskin or jico leather mat

To do this, the platter pad has to have the same durometer as the vinyl itself.

Just not true. This again is where intuitive/rational/objective/measurement based talk diverges from something called "listening". A platter pad with the same durometer as vinyl (is there such a thing as "the vinyl"?) may sound best with one turntable/arm/cartridge combination while a copper, cf, or bare aluminum (as Harry Weisfeld advocated for years with his turntables) may sound best with others. I prefer the sound of no platter mat with my two decks. 

Go with the leather is my advice. If nothing else, it looks sexy. 

@lohanimal 

Halcro uses the pigskin mat in conjunction with the Victor Glass mat.

The Jico pigskin was a limited run some years ago.

The key is the thickness - the Victor and Jico are much thinner than most leather mats.

Best place to find the Vitor mat is on Yahoo Japan - they usually sell for around $50USD and come up from time to time. Topclassaudio has an original  Victor Glass mat and pigskin leather mat set for sale currently.

A friend based in the UK has produced their own CNC cut Leather Mats in 1.3mm thick leather.

Is there a specific diameter that is needed?

Size of a 12 inch record I guess 😂 who are they

Just not true. This again is where intuitive/rational/objective/measurement based talk diverges from something called "listening". A platter pad with the same durometer as vinyl (is there such a thing as "the vinyl"?) may sound best with one turntable/arm/cartridge combination while a copper, cf, or bare aluminum (as Harry Weisfeld advocated for years with his turntables) may sound best with others.

@fsonicsmith FWIW, when I first heard a proper platter pad designed around the points I previously mentioned, measurements didn’t come into it for many years- it was all about the listening as you say! To your point: every turntable we tried the mat on sounded better than every turntable that didn’t have the mat; it was making a bigger difference than the cartridge, arm or turntable itself! IMO its a real shame its not made any more! The designer (Warren Gehl of ARC who spent many years designing it) of the mat once told me that the hardness of the mat is a key factor. This suggests that one could make a reasonably good mat if it were simply pressed of vinyl and otherwise had materials embedded (as his mat did) that also provided damping properties.