Designing and synthesizing flawless two-dimensional polymers (2D-Ps) via meticulous molecular preorganization presents an intriguing yet challenging frontier in research. We report here the single-crystal-to-single-crystal (SCSC) synthesis of a 2D-P via thermally induced topochemical azide-alkyne cycloaddition (TAAC) reaction. A designed monomer incorporating two azide and two alkyne units is synthesized. The azide and alkyne groups are preorganized in the monomer crystal in reactive geometries for polymerizations in two orthogonal directions. On heating, the polymerizations proceed in a hierarchical manner; at first, the monomer reacts regiospecifically in a SCSC fashion to form a 1,5-triazolyl-linked 1D polymer (1D-P), which upon further heating undergoes another SCSC polymerization to a 2D-P through a second regiospecific TAAC reaction forming 1,4-triazolyl-linkages. Two different linkages in orthogonal directions make this an architecturally attractive 2D-P, as determined, at atomic resolution, by single-crystal X-ray diffraction. The 2D-P reported here is thermally stable in view of the robust triazole-linkages and can be exfoliated as 2D-sheets.