I don't know but it looks to have some kind of defect that is limiting and/or deforming the petals.
Might it be in the rudbeckia/coneflower/sunflower/coreopsis family?
The cone probably will help id the plant since it is more symetrical in design than the above mentioned.
I've had weird problems with deformities to rudbeckia blossoms(newer variety) and dieback funguses on common blackeyed susans this year.

Thanks for your input Dottie. I found out a little more info. They bought it at a local plant sale, it was labeled green coneflower.

Ginger

hmm- wonder if it's one of the green eyed rudbeckies? the cone doesn't look quite right, but then it doesn't look like a coneflower cone, either. Reminds me more of a ratibida cone, though squatty, and they do have sparse petals. Wonder if it's some ratibidia species? Common name for the normally found ones is mexican hat. Leaves don't look the same, though.

After searching the internet, we have decided it might be some form of a green headed coneflower.
Thanks for your help!

Here is a link that might be useful: green headed coneflower

which are actually rudbeckias, just to confuse everyone :)