I am not expecting to get to species level, there are 76 species in the Rio State!
From most of those there is no material on the web I could compare it with, and on top again I have no flowers.
But would just want a confirmation that it is a Peperomia sp.

It reminds me a bit of one I used to have Peperomia trinervula

Peperomia nitida appears to have only two long veins running the length of the leaves ..

https://sites.google.com/site/...

But check on Flora do Brasil, one photo shows more.

Look at the photos of Peperomia alata on Flora do Brasil, the shape and venation looks correct. The reddish colour on the leaf joints seems to be present (use a zoom feature on first photo), that could be variable. I've only checked those with photos on the site.

There's a dried specimen which shows the leaf shape, note how the tip extends often with a slight indentation, that is the leaf edge doesn't gradually curve to the tip.

http://media.eol.org/content/2...

I had seen those photos of Peperomia alata on the Flora do Brasil, Janet, but didn't get that feeling of 'yes, that's it!', it could be that one though as you say the venation is correct and the leaf shape too not only in your second link with the dried specimen but also in the photo's of the Floro do Brasil, the leaf joints are a very faint red, mine has bright red ones, but can be due to variation and growing conditions, (I suppose that's how they select cultivars in a specie)
[quote]the leaf shape, note how the tip extends often with a slight indentation, that is the leaf edge doesn't gradually curve to the tip./quote]

After looking into this again, and more searching, I think you're right Janet, The photos on the Flora do Brasil are poor quality so maybe that's why it didn't convince me, but all the essential elements like you pointed out are there.
I'll mark this as closed.