  Polytypism of incommensurately modulated structures was hitherto unobserved.
Here, we found the phenomenon in simple halogen systems of bromine and iodine
upon molecular dissociation in the solids under pressure. Single-crystal
synchrotron X-ray diffraction in laser heated diamond anvil cells pressurised
up to 112 GPa revealed a number of allotropes of bromine and iodine including
polytypes of Br-III{\gamma} (Fmmm(00{\gamma})s00) with {\gamma} varying within
0.18 to 0.3.
