Garry was right. There is a round plastic plug at the rim. After removing the plug I determined that I couldn't get a socket over the nut unless I had some kind of ratchet extension with u-joints - which I don't have and don't want to buy.
Eventually, after several skinned knuckles, I was able to remove the nut from the rear by sighting down through the hole and attacking it with a ratcheting box wrench.
Now, after removing and looking the toilet over, I think I'll replace it rather than repair it. I see where there are a couple of threads on this topic so I'll read them first before I ask any more questions.
Thanks to all who helped.