What used to be called Notocactus buiningii is now more properly referred to as Parodia buiningii. (Names and classifications have a habit of changing in the cactus world.)
According to Edward F. Anderson in his encyclopaedic work, The Cactus Family, Parodia buingingii is found close to Santana do Livramento, which is in Brazil, and Rivera, a neighbouring locality in Uruguay. The book also states that the cactus is reported to be rare. Well, it's often seen in the garden centres around here, so perhaps the book refers only to its occurrence in the wild.
This particular specimen is 14 cm in diameter and 9 cm tall, with 15 ribs. It currently shows 12 flower buds, 7 of which are already blooming. Actually, they only bloom when the sun "wakes them up" with a direct hit in the morning, and close up tightly again in the late afternoon, when shade returns to the plant.
Other cacti to show flowers are the members of the Mammillaria and Echinofossulocactus families. There are too many to show all the different varieties, so here are just one from each family.