Mammillaria haageana Pfeiff.
These cacti are native to southern Mexico.
Identification: Plants are spherical in shape, usually occurring alone, sometimes in clusters, up to 6" (15 cm) high and 4" (11 cm) wide. Spine groups on the side are arranged in a spiral pattern (instead of as vertical rows as in many other cacti), and they are closely spaced. Radial spines are in groups of 18-30, smooth, white, and bristled. They are ¹/₁₆-³/₁₆" (3-6 mm) long. Flowers range from bright purple-pink to carmine. Fruits are red.
If you look closely at the photo at right, you'll notice that in 1979 this cactus was labelled Mammillaria elegans dealgata. When I first saw this name, I surmised that some droll botanist had perpetrated a small joke on the botanical community. What else could Mammillaria elegans possibly mean other than "nice boobs?" I was partly right. Mammillaria does refer to breasts, specifically nipples, and elegans means "elegant." But in this context, Mammillaria refers to the tubercules on the plant surface, small raised bumps arranged in spiral patterns, the base of each group of spines. In most cacti, these are arranged as a series of vertical ribs along the stem of the cactus, but in Mammillaria, they follow the Fibonacci number sequence, a pattern that is also common elsewhere in nature.
This genus has an unusual approach to plant metabolism, absorbing CO₂ at night and re-emitting it during the day, in a way that improves photosynthesis. This is called Crassulacean acid metabolism, and it is a trait these cacti have in common with pineapples.
The Mammillaria Forum (superb photos)
Mammillaria haageana description by Thomas H. Kent, last updated 25 May 2020.