Convert between rhombohefral and hexagonal cells

Rhombohedral cell parameters:
cell dimensions (a=b=c) , angles (alpha=beta=gamma)

Hexagonal cell parameters:
cell dimensions (a=b) (c) , angles (alpha=beta=90, gamma=120)

Reindex from an R-cell (hkl) to a hexagonal cell (HKL):

Conditions limiting possible reflections: