Information from Britton & Rose II 124. 1923 reveals under Acanthocereus
pentagonus ( A. tetragonus now considered more appropriate
see Cactus Lexicon 2006):
Cereus quadrangularis Haworth (Syn. Pl. Succ. 181. 1812; C.
trigonus quadrangularis Pfeiffer, Enum.Cact. 118. 1837; Cactus
quadrangularis Loudon, Encycl. Pl. 412. f, 6876. 1829) may belong
here, but Pfeiffer referred it with a question to Cereus caripensis
De Candolle (Prodr. 3: 467 1828 ; Cactus caripensis Humboldt,
Bonpland, and Knuth, Nov. Gen. et Sp. 6: 66. 1823) but this species
was referred by Schumann to the genus Rhipsalis.
Pfeiffer refers to drawings in Plant Amer Plumier ed Burm. 1755 which
clearly shows it is not a Rhipsalis!
Cactus caripensis is treated as a synonym of Rhipsalis
cassutha in B&R 1923
In other words there is no such thing as Rhipsalis quadrangularis
even though Schumann’s treatment suggests it could well be. BUT
the name persists in horticulture. We consider it to be a cultivar of
Rhipsalis micrantha .