Leuchtenbergia principis

Leuchtenbergia principis (agave cactus or prism cactus), the sole species of the genus Leuchtenbergia, is a species of cactus. It is native to north-central Mexico (San Luis Potosi, Chihuahua). The genus is named after Maximilian Eugen Joseph (1817–1852), Duke of Leuchtenberg and amateur botanist.
It is very slow-growing but can eventually grow up to 70 cm high, with a cylindrical stem which becomes bare and corky at the base with age. It has long, slender, grayish-green tubercles 6–12 cm long, with purplish-red blotches at their tips. The tubercles are topped with papery spines, making the plant resemble an agave; old, basal tubercles dry up and fall off. After four years or so, yellow, funnel-shaped flowers 5–6 cm diameter may be borne at the tubercle tips. The fruit is smooth and green, 3 cm long and 2 cm broad. It has a large, tuberous taproot.

Because they're adapted to grow in the shade of other plants, Leuchtenbergia is perfectly able to survive without a lot of direct sun. The tubercles can move around a bit, depending on the light and humidity: they'll lie flat if there's too little light, and pull closer together and more upright if the air is exceptionally dry. So if you notice that your plant's lying flatter than it was when you bought it, well, that's one possible reason why.