Spin-frustrated polyoxometalates, K11H[(VO)(3)(SbW9O33)(2)].27H(2)O (1) and K-12[(VO)(3)(BiW9O33)(2)].29H(2)O (2), containing approximately equilateral and isosceles (VO)(3)(6+)-triangles (V-IV...V-IV separation of 5.4-5.5 Angstrom) sandwiched by two diamagnetic alpha-B nonatungstate ligands ([SbW9O33](9-) and [BiW9O33](9-)) with approximate D-3h symmetry, are found to show magnetization jumps with distinct hysteresis for the S = (1)/(2) <----> S = (3)/(2) level crossing under fast sweeping pulsed magnetic fields (similar to10(3) T/s) at T less than or equal to 0.5 K. This unusual phenomenon is attributed to the theoretical prediction of half step magnetization, which is expected for an antiferromagnetic spin triangle with antisymmetrical Dzyaloshinky-Moriya interaction. The degeneracy of the S = (1)/(2) states for 1 is removed by slightly lower symmetry effects of triangular structure for 2. The calorimetry of 1 and 2 shows the heat capacity anomaly at 2 less than or equal to T less than or equal to 20 K which is associated with a thermal excitation from the S = (1)/(2) ground states to the S = (3)/(2) state at zero field. Zero-field splitting energies (5-7 K) between S = (1)/(2) and S = (3)/(2) states for 1 and 2, readily estimated by the level-crossing field for the magnetization, allow us to measure the hyperfine-structural 22 lines due to three equivalent l = (1)/(2) V-51 nuclei, the fine-structural triplet line of the S = (3)/(2) excited state, and the g anisotropy on the high-frequency ESR spectra. The spin-frustrated (VO)(3)(6+)-triangle for 1 and 2 is a good model of the magnetization between pure quantum states S = (1)/(2) and (3)/(2) and provides a new class of single-molecule magnets.