This data was collected to study the growth and relaxation dynamics of an icosahedral quasicrystal from a liquid. The composition of the imaged QC is Al-19at%Pd-10at%Mn, and the growth and relaxation dynamics of an icosahedral quasicrystal were observed under slow cooling conditions. The quasicrystalline phase shows weaker projection intensity because of more X-ray absorption resulting from its heavy elemental (Pd and Mn) composition. This contrast difference allowed us to segment the quasicrystal from the liquid phase and visualize the 3D volume of the icosahedral quasicrystal. During the growth, a pentagonal dodecahedral shape with 6 five-fold facets was clearly visible growing from the oxide skin (Al2O3) into the liquid. Facet velocities are noticeably anisotropic with facets perpendicular to the gravitational field growing faster than facets further away from gravity. Growth is clearly bulk transport limited. Near equilibrium, we observe a morphological transformation to a truncated dodecahedral shape characterized by the truncation of five-fold vertices in the growth shape (pentagonal dodecahedron) into triangular facets. This signifies a relaxation mechanism to a lower energy equilibrium shape in this icosahedral quasicrystal thus the growth and equilibrium shapes in icosahedral QCs are not identical. For details on the resulting 3D reconstruction, visualization, and kinetic analyses, the readers are encouraged to look up the following publication.