Amorphous ices govern a range of cosmological processes and are potentially key materials for explaining the anomalies of liquid water. A substantial density gap between low-density and high-density amorphous ice with liquid water in the middle is a cornerstone of our current understanding of water. However, we show that ball milling "ordinary" ice Ih at low temperature gives a structurally distinct medium-density amorphous ice (MDA) within this density gap. These results raise the possibility that MDA is the true glassy state of liquid water or alternatively a heavily sheared crystalline state. Notably, the compression of MDA at low temperature leads to a sharp increase of its recrystallization enthalpy, highlighting that H2O can be a high-energy geophysical material.