This is Cochemiea / Mammillaria poselgeri.
The planter has a diameter of 10"/25cm.
It is one of 5 cactus species in a small genus endemic to Baja California. The genus is named after the original people living in the area. Some authors include the genus in Mammillaria. Cochemiea species differ by having zygomorphic, tubular flowers pollinated by hummingbirds. Cochemiea poselgeri is a wanderer from the start; the other species are commoner in collections because they stay tightly clumped for a long time.
Mammillaria is a huge genus of cacti, and there are far more published names than valid species. Most are from higher elevations. They may struggle in hot sun, high humidity or climates with warm to hot summer nights. Those from Baja California tend to tolerate these conditions well, and flower every few weeks through the summer here in Phoenix. Baja California has hot deserts, frequent high humidity, and rain at any time of year. Weather is hot year-round, except right on the coast, or in the mountains. Most other cacti are native to areas with strongly defined summer-only rainfall patterns, and flower once a year. Most Baja plants of all types, including cacti, will grow and flower whenever a rare rainstorm passes by in habitat.
If you live in a typical temperate climate, or a hot and humid Southern climate, and have had trouble with Mammillaria rotting during hot and humid weather, try growing one of the more readily-available Baja Mamms: M. fraileana, M. schumannii or one of the Cochemiea species. They do best in full to near-full sun, and require excellent soil drainage. When I lived in St Louis I grew them in large particle traction sand. Some people use turkey grit. If you use a standard "cactus mix" based on peat moss or sawdust, you will need to repot every 2 years, or the mix compacts and becomes rotten. This kills cactus roots.
In 1991 I stayed at Hotel Rancho Buena Vista on the Gulf side of the Baja California peninsula. This is a fishing hotel for sportsmen; it is not at all fancy, but ladies would feel comfortable there, too. The beachside bar in current photos looks the same as it used to.
Hotel en Baja California
The hotel had plants of this species growing in planters along the driveway. I collected a few ripe fruits, brought them home and grew the seeds. This is one of those plants. It flowers throughout the summer, and produces fruits. The branches eventually get too long, and break off. They root easily and form new plants. If you'd like to try and grow it from seed PM me. It's not hard, but it's not like growing radishes.
I also have a Pachycereus pectenaboriginum from seed I brought back from a different Baja fishing trip. It is much taller than I am, despite having had the growth tip frozen multiple times through the years. It hasn't flowered yet.