These are a funny looking small barrel-like cactus that can grow to around 3″. Dark purple in full sun. Partial shade in the heat. I love the slightly dessicated look in the summer, all wrinkly. When they are full of water, they are less interesting.
Keep blooming all summer long. Well, I suppose if you traveled with them in October to Australia to catch a 2nd summer in a row then maybe they’d be pretty fed up and would stop blooming before the end of the endless summer. But I can’t be sure.
This cultivar is called “Henry’s Bookcase”. I don’t know why.