Escher-Style Tessellation

Symmetry groups, wallpaper patterns, and interlocking tiles

TILING TYPE

■ Square (p4m — 4-fold symmetry)
⬡ Hexagonal (p6m — 6-fold)
△ Triangular (p3m1)
⬡ Escher Fish (p6)
■ Escher Birds (p4g)

STYLE

70
0.35
0.85

SYMMETRY INFO

p4m: Square lattice with 4-fold rotation and mirror symmetry. 4 rotations, 4 mirrors. Point group D₄.
About: There are exactly 17 wallpaper groups — symmetry groups of periodic plane tilings (Fedorov 1891, Pólya 1924). Escher studied these groups in 1936 at the Alhambra and used all 17 in his work. His method: start with a regular tiling, replace each straight edge with a curve (using slide/rotate/glide rules that preserve periodicity), and interpret the resulting shapes as animals or objects. The constraints ensure the modified tiles still tessellate. Square tilings admit 4-fold rotational symmetry (p4, p4m, p4g), hexagonal 6-fold (p6, p6m), and triangular 3-fold (p3, p3m1, p31m).