Phononic crystals offer unique band structures for acoustic wave propagation. Fabricating intricate threedimensional phononic crystals allows a new class of devices with complex phononic band structures beyond capabilities of two-dimensional designs. We have successfully fabricated novel 3D phononic crystals with 1 mm lattice constant and minimum feature sizes as low as 100 micron using high-resolution stereolithography printing. Here we report the first theoretical calculations and experimental results demonstrating wide complete 3D phononic band gaps not attainable by corresponding 2D structures with the same lattice geometry. Longitudinal and shear wave propagation is suppressed by more than -60 dB in frequency bands as wide as 400 kHz to 1 MHz.