Complex sentence: On New Year's Eve, the Square dreams about a visit to a one-dimensional world (Lineland) inhabited by "lustrous points", in which he attempts to convince the realm's monarch of a second dimension; but is unable to do so.
Split into simpler sentences: On New Year's Eve, the Square dreams about a visit to a one-dimensional world (Lineland) inhabited by "lustrous points". Thus, the Square attempts to convince the realm's monarch of a second dimension; but is unable to do so.