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 .