The Cactaceae
The Cactaceae are a family of generally spiny, succulent plants with leaves that are either early-deciduous or not produced at all. The succulent stem conducts photosynthesis and stores water.
The flowers have
Dr. Kenneth R. Robertson, from illinois, has put together an excellent online synopsis of the Cactaceae. Please read through this information by clicking on the link below and navigating through the 17 short pages on the Cactaceae. (Click the "[Next]" links on each page to move to the next page.)
https://www.life.illinois.edu/help/digitalflowers/Cactaceae/1.htm
Although a few members of the Cactaceae have large leaves, most do not. If leaves are produced at all, they are tend to be small and early-deciduous.
The bases of the perianth parts and the stamens are fused together. (The arrow below shows the fused bases of the perianth parts and the stamens.) After flowering, this part of the flower falls off, leaving the inferor ovary, embedded in stem tissue, behind.
Below are images of four species
Species #1:
Species #2:
Species #3:
Species #4: