The genus Frailea, placed in the Cactaceae family, is named after the Spaniard, Manuel Fraile who looked after the cacti collection of the US Department of Agriculture. Frailea species are all small solitary or clustering plants with flattened round bodies that rarely exceed 5cm in diameter. The plants have few to many very shallow ribs which may be straight or wavy. The spines are quite small and weak if present at all and pose little threat to the finger tips. The yellow flowers are often larger than the bodies and open in the heat of the day for a short time, if at all. Frailea species are cleistogamous, meaning that often times the flowers do not even emerge, but rather they self-pollinate while still inside the plant. They are well suited to pot culture and do very well in rockeries.

Frailea grahliana grows on flat sandstone at the edge of plate rocks, or on clayey soil among sandstone fragments, both in open and sunny spots or under grasses. The climate is warm and humid with hot summers and much thaw during the night. The winters are also warm even so occasionally light frosts may occurs, but the sandstone rocks warmth during the day and give off heat at night so rarely the temperature at soil level go below 5°C. It grows in association with Bromelia serra, Cererus lanosus and Monvillea sp. (paxtoniana?) that forms snake like stems. Fraileas are cleistogamous meaning that their flowers produce seed without even opening. Without the need for pollination the buds rarely reach full bloom and remain closed. They will open only in great heat in the hottest, brightest, afternoon sun, if at all. Luckily this rare species is pretty enough that one can forgive it for not always displaying its flowers.