The simplest name to apply to this plant is the common one: rainbow hedgehog cactus. I made an attempt to figure out the most recent accepted scientific name and had to abandon it. “billy liar” stated this plant’s name was Echinocereus rigidissimus var. rubrispinus (the varietal epithet meaning red-spined), but when checking the nomenclature, I ran into a few problems. The USDA Plants Database entry on Echinocereus rigidissimus doesn’t subdivide the species into subspecies or varieties. However, the distribution of this taxon extends from southwest USA into Mexico, so it is quite possible that the variety rubrispinus only occurs in Mexico, and so wouldn’t be covered in the USDA database.
This does seem to be the case after browsing through Echinocereus Online where it lists the taxon Echinocereus pectinatus var. rubispinus as occurring in Chihuahua, Mexico. This reference suggests that Echinocereus rigidissimus var. rubrispinus is an outdated name. However, looking back at the USDA database, it seems those taxonomists would make the opposite conclusion, based on their listing of Echinocereus pectinatus var. rigidissimus as a synonym for Echinocereus rigidissimus. Conclusion? Confused.