I agree that it's a Cactus Basket. The quilter just left off the pedestal pieces and set them four together. It's a nice look. I believe I've seen that variant before but I don't remember if it had a different name. Nancy Cabot printed the pattern in 1933. If you scroll down the page to the picture of the sections before they're assembled, you can see it.
http://nancycabotsewalong.blogspot.c...ilt-block.html