The outer hard enamel layer of your teeth is acellular and cannot regenerate after it forms. Its been a while since I worked in this field (my PhD) but the inner dentin has some ability to regenerate due to the adjacent cells in the pulp. I'm not really sure I understand what the previous comment is saying about the crystal structure. All of the tooth (enamel and dentin) and bone mineral related carbonate "hydroxyl" apatite is crystalline with some additional amorphous material in between.