No, I'm not absolutely sure. I have only self-education in biology/horticulture. The wikipedia article on polyploidy is unhelpful on the matter. But I have always wondered what kind of weird sex is going on if three partners have to come together, I've never heard of that happening in general. So I am very attracted by the theory that the third is only to pollinate the second, which is repeated at many sources.

But the most reputable horticultural sources I can find seem (emphasis on seem) to say that two varieties are desirable (desirable, perhaps not entirely necessary) just to pollinate the triploid:

Brogdale http://www.brogdale.org/choosepollination.html says "To produce fruit the triploid will need two pollinators" (that seems definitive, no fruit on the triploid without two pollinators, and Brogdale is our national apple archive)

RHS http://www.rhs.org.uk/advice/profile...tionGroups.pdf
says "Some cultivars are triploid – they have sterile pollen and need two other
cultivars for good pollination" (actually you could read that both ways - good pollination of what - but the plain reading is that two are needed for good pollination - note good pollination - of the triploid)

Keepers Nursery http://www.keepers-nursery.co.uk/sea...aspx?id=BRASEE says "Bramley's Seedling is a triploid variety and should be grown with two other pollination partners" (again you could take that both ways as with RHS - Keepers Nursery has the largest number of apple varieties of any commercial nursery)

The BBC say two for the triploid too, but I don't consider them reputable.

Searching the web, I found one lady who posted on a forum with a problem. She had a triploid, and cut down one of the two pollination partners. The next year, she only got "crabs" on her triploid. Perhaps it was a bad year, perhaps the one she left wasn't a good pollinator for it. Who knows. No one answered her post. She didn't update us the following year, at least not on that thread.

This source http://web.ukonline.co.uk/suttonelms/apple27.html points out that an experiment in 1938 by Crane and Lawrence found 5% self-fertilisation on triploids, which is more than on most diploids. Which rather goes against the received wisdom. What is going on? The same source goes for the third to pollinate the pollinator theory.

This source, which seems well-grounded in real life practice in the orchard, goes for the third to pollinate the second theory. http://pollinator.com/effecpol.htm But it makes an interesting point about an individual fruit needing to be well pollinated in order to grow large, in other words apples, unlike people, can be half pregnant. So perhaps that is what the third variety is about, and why the lady above got small fruit on her triploid.

btw, I was wrong in saying that Cox's Orange Pippin is a triploid, it isn't. It was Blenheim Orange that I had in mind.