page_title: Hexacontatetragon
section_title: Symmetry
hierarchical_section_title: Hexacontatetragon / Symmetry
caption_attribution_description: English: en:hexacontatetragon symmetries
context_page_description: In geometry, a hexacontatetragon or 64-gon is a sixty-four-sided polygon. The sum of any hexacontatetragon's interior angles is 11160 degrees.
context_section_description: The regular hexacontatetragon has Dih₆₄ dihedral symmetry, order 128, represented by 64 lines of reflection. Dih₆₄ has 6 dihedral subgroups: Dih₃₂, Dih₁₆, Dih₈, Dih₄, Dih₂ and Dih₁ and 7 more cyclic symmetries: Z₆₄, Z₃₂, Z₁₆, Z₈, Z₄, Z₂, and Z₁, with Zₙ representing π/n radian rotational symmetry.
  These 13 symmetries generate 20 unique symmetries on the regular hexacontatetragon. John Conway labels these lower symmetries with a letter and order of the symmetry follows the letter. He gives r128 for the full reflective symmetry, Dih₆₄, and a1 for no symmetry. He gives d (diagonal) with mirror lines through vertices, p with mirror lines through edges (perpendicular), i with mirror lines through both vertices and edges, and g for rotational symmetry. a1 labels no symmetry.
  These lower symmetries allows degrees of freedoms in defining irregular hexacontatetragons. Only the g64 subgroup has no degrees of freedom but can seen as directed edges.
caption: Symmetries of hexacontatetragons
exif: {}