It certainly is a member of Aizoaceae, commonly called Mesembs round here.
Could it be a Lapidaria?

I tried to look it up under those names but so far nothing. So I posted at a Mesembs group and see if anyone over there knew what it was. I thought it looked kind of like a vineing split rock. So we will see. I am posting a better picture of it. Click on the pictures to get the full size picture.
Stevi

Here is a link that might be useful: Little unknown one

I have it also. Never find the right name: some said it's Delosperma lehmannii, some said it's corpuscolaria lehmannii. The problem is that Delosperma have hairy leaves (this one, no!).
Another thing, is that I got another one, same thing, just longer leaves. Now I got a problem: I can't find the new one on Corpuscolaria's, only on Delosperma taylorii.
I know it's not a Delosperma! I'm not sure if it's a Corpuscolaria...
(http://www.mytho-fleurs.com/images/jardins_botaniques/bochum/delosperma_lehmannii.JPG)
Better I'll wait until will flowers.
Please let me know if you find the right name for yours!

Good luck,
Rodica

P.S. It's hard with Aizoaceae, but they look fantastic! Can't help myself!

Here is a link that might be useful: Corpuscolaria (Delosperma) lehmannii?

Delosperma don't have hairy leaves (Delopserma echinatum is a strange one that has bristles on the leaves). Some of them have pappillose leaves, some of them don't. The genus is much more varied than the Iceplant many people have in their garden.

Your plant (Rodica's plant) I'm not sure about. It may be a Gibbaeum.

Here is what Steve Brack of Mesa Gardens had to say in the brackets.
Here is a link to another picture of D.lehmannii and it looks just like what I have. So for now I am going to stay just a bit confussed.
Stevi
[[There are a lot of these little mesembs, so just keep looking in Delosperma
or Corpuscularia. The literature is not complete because these plants grow
in huge numbers of little colonies, someone could have collected something
or some seeds and they are not all published and described. It is not like
several collections I have of Delo lehmannii, so try D taylori and see how
it compares. Steven Brack, Mesa Garden]]

Here is a link that might be useful: D.lehmannii