It is a Christmas Cactus.
The leaves (stems) are neither wide nor flat, but thanks for guessing. I
suppose I would've described if I'd known the picture was so poor it
could've been mistaken for Schlumbergera.
The mature stem segments are about 2 - 2.5" each, average 1cm wide, are
"angularly cylindrical" with four deep ribs, and have stiffened tufts of
scant hairs. Flowers are terminal, and in my case in both senses of the
word. I was so looking forward to seeing what they looked
like - if for no other reason than to at least identify it! I'm so
disappointed & want to know what I did wrong. The RH in here isn't much
above 40%, but I had brought it indoors at least 6 weeks before there was
any sign of budding. For a great many plants that's long enough to acclimate
themselves, isn't it? The buds grew to only about 5mm, got nice & pink then
easily fell off when I only barely moved the pot.