More Backyard Fun - Identify the Fungus!

I found this curious thing in my backyard last night. I thought it was an old styrofoam ball, perhaps a dog's toy tossed over the fence from another yard. I looked and felt like styrofoam, but as I pressed a part of it, I realized it felt more decomposed than modern plastics probably would be. So I stuck in my thumb and pulled a chunk off. The outer body was yielding like a mushroom, breaking under pressure, while the inside was soft like marshmallow. The fungus smell came up immediately, mild and very much like that of the white mushrooms you'd buy at the store. No, I didn't taste it...

There was a clump of dirt near the faint evidence of where the stem would have to have been. It must have grown on the ground, but I found it on some gravel and could find no trace of its stem.

Can you identify it? I've found references on the web that lead me to believe it's some kind of puffball; but all the pictures I've found show smooth-shaped balls, while this one has ridges on one side.

Thanks!

Dave