Abstract A new selected area electron diffraction (SAED) pattern was found from Fe‐illite. The lattice of the ED pattern can be described as a compound tessellation of (3,6)79{3,6}], which is based on a large coincidence‐site lattice (CSL) with oriented crystal associations rotated by a non‐crystallographic angle 26°. This phenomenon corresponds to the plesiotwinning of Fe‐illite and has been never reported in the nature so far.