A simple iterative arrangement of cubes leads to a visually rich and complex fractal crystal with an overall regular-octahedron convex hull and infinitely many facets. Each facet is essentially a Sierpinski triangle, and the vertex of a cube just touches the center of each triangular hole. This fractal crystal is constructed by starting with a first generation cube and placing a half-scale cube on the center of each face. The second-generation cubes have the same orientation as the first-generation cube. Third-generation cubes again scaled by half are placed on each unoccupied face of a second-generation cube. This process is continued ad infinitum to form the fractal crystal. Some related constructions created using other Platonic Solids are described as well.