The student pilot reported that he hover taxied the helicopter to land on the ramp and executed a 180° pedal turn to face the center of the ramp. When the helicopter landed, he reduced the throttle to idle, and the helicopter began to shake. A flight instructor who was watching the landing from across the ramp communicated over the radio and via hand signals, telling the pilot to pick the helicopter up to a hover. The student pilot attempted to increase the throttle and increase collective to pick the helicopter back up to a hover, but the helicopter began to shake violently, and the student pilot reduced the collective but was unable to regain control. A review of a surveillance video provided by the operator revealed that the helicopter began to rock on its skids, rotated about 180°, and rolled over on its left side, which resulted in substantial damage to the main rotor blades, tail rotor blades, tail boom, and fuselage. The student pilot reported that there were no preaccident mechanical failures or malfunctions with the helicopter that would have precluded normal operation.