This data was collected to study the principles of the growth and melting of a decagonal quasicrystal from a liquid. The composition of imaged sample is Al-9.55at%Ni-9.55at%Co, and the growth and melting of a decagonal quasicrystal were observed during the continuous slow cooling. The quasicrystalline phase shows weaker projection intensity because of more X-ray absorption resulting from its heavy elemental (Ni and Co) composition. This contrast difference allowed us to segment the quasicrystal from the liquid phase and visualize 3D volume of a decagonal quasicrystal. During the growth, the ten facets of the quasicrystal were clearly seen. On the other hand, marked interface curvature was observed during the melting, such that the quasicrystal eventually lost its ten habit planes. In addition, the growth rate is nearly constant for every facet; however, the melting rate is shown to depend on the physical orientation. Therefore, the growth and melting processes do not have time-reversal symmetry and different mechanisms are applied to explain this behavior. To determine the underlying mechanisms of the microstructural evolution, we analyzed the projection intensity and correlated it to the phase diagram. The 3D visualization and projection intensity analysis proved that growth is governed by first-order kinetics due to interfacial attachments and the melting is affected more strongly by gravity-driven convection. For details on the resulting 3D reconstruction, visualization, and kinetic analyses, the readers are encouraged to look up the following publication.