Multi-valued versus single-valued large-amplitude bending-torsional-rotational coordinate systems for simultaneously treating trans-bent and cis-bent acetylene in its S1 state

► Multiple-valued and single-valued coordinate systems are compared. ► Coordinate ranges are illustrated by portions of squares and cubes. ► Multiple-valued symmetry properties become single-valued boundary conditions. ► To avoid quasilinear complications, triatomic molecules are excluded from consideration.