The phase study of a Cd-Yb 1/1 approximant crystal over a wide pressure and temperature range is crucial for the comparison study between periodic and quasiperiodic crystals. The Cd(4) tetrahedra, the most inner part of the atomic clusters, exhibited various structural ordering in the orientation sensitive to pressure and temperature. Five ordered phases appeared in a P-T span up to 5.2 GPa and down to 10 K. The propagation direction of ordering alternated from [110] to <111> to at about 1.0 GPa and again to [110] at 3.5-4.3 GPa. The primarily ordered phases that appeared by cooling to 210-250 K between 1.0-5.2 GPa further transformed to finely ordered ones at 120-155 K. Besides the original short-range type interaction, a long-range type interaction was likely developed under pressure to lead to the primary ordering of Cd(4) tetrahedra. Coexistence of these interactions is responsible for the complicated phase behavior.