Dear friend, I do admire and respect the seriousness, with which you reffer to the plants you love!
I personally have only one big and round cactus plant, which has created many "babies" attached around their "mom". In late Spring a young friend carries it on a sunny spot on our terrace. It is quite heavy to carry it myself, because of the plant itself and not its pot! During the winters it is placed in my heated green house, together with some other sensitive plants.
But ,no! I don't even know its name! I only admire its magnificent flowers , which look like very delicate and transparent pink Day Lillies. Each bloom lasts only one day , but imagine about eleven of these blooms opening almost together!
As you understand, I almost have no idea of cacti and succulents, except of the right way to feed them and water them. BUT! I checked a little in the internet AND in my books. Just because I admire your serious approach and love for your plants! In my books with no specific success. But in the internet, I found this site , where you can very possibly have an answer:
www.succulent-plant.com/home.html
In the bottom of this page, you will see some underlined red sentences. Go to " Cactus and Succulents by Genus or Type". I think you will find it really interesting, because it includes beautiful pictures for you, in order to compare with your own beautiful plant.
Good luck, Karen!
P.S.
I prefer the "Desert Rose " link.
"..So,perhaps, it is easiest, through awareness of flowers in particular, of their radiant beauty and purity, their vibrant colour, to come to the excellence of the One and be uplifted beyond thought to our divine selves".Dorothy Maclean