Called Elephant's Tooth, or more commonly, Dumpling Cactus, the C. elephantidens is a globular cactus that readily clumps. It is sometimes listed as Mammillaria recurvispina. This is a good cactus for USDA Zones 9b-11, but does require light shade during Phoenix summers.
I have not yet placed this cactus in my landscape, but when I do, it will probably be next March, and it will be planted in the dappled shade of one of the Mesquite trees. I have quite a few cacti that require light shade in summer, and I'm running out of room to place them all! Another problem with planting them near the trees is that they end up with a lot of tree litter, both on and around the cacti. It's very hard to remove because the spines catch the fallen leaves and flower litter. I think this litter detracts from the beauty of the cacti, but I deal with it as best I can in order to have cacti from other regions of the world.
This cactus usually blooms in late summer, so this late flower is a real treat this time of year. Up until today, we've had triple digit temperatures, so maybe this cactus didn't realize it isn't summer any longer. Most sources say the flowers are very fragrant, but this flower has no scent at all. I recently watered this cactus, and don't expect to water it again until mid-November. As even cooler temperatures come, I will cut back even further and water it about every six weeks.