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Both well known crystal structures  m -Co 4 Al 13  and  o -Co 4 Al 13  are described in a simplified two-dimensional representation of regular pentagons and prolate rhombs. The dichromatic tilings differ in the periodic arrangements of prolate rhombs (brick-like and parquet-like, respectively) but show the same matching rules for the regular pentagons. The 2D scheme is used to show the variety in combination of these structural fragments that leads to related periodic as well as cyclical tilings. Starting from different initial nuclei, cyclical tilings with point group symmetry C 5v  or C 10  are related to multiple twinned arrangements of the structure  m -Co 4 Al 13 . Different decorations of these tilings are compared and characterised by their symmetry.

Mosaic-like tilings derivated from o -Co 4 Al 13 and m -Co 4 Al 13 crystal structures