page_title: Hendecagon
section_title: Symmetry
hierarchical_section_title: Hendecagon / Symmetry
caption_attribution_description: English: en:Hendecagon symmetries
context_page_description: In geometry, a hendecagon or 11-gon is an eleven-sided polygon.
context_section_description: The regular hendecagon has Dih₁₁ symmetry, order 22. Since 11 is a prime number there is one subgroup with dihedral symmetry: Dih₁, and 2 cyclic group symmetries: Z₁₁, and Z₁.
  These 4 symmetries can be seen in 4 distinct symmetries on the hendecagon. John Conway labels these by a letter and group order. Full symmetry of the regular form is r22 and no symmetry is labeled a1. The dihedral symmetries are divided depending on whether they pass through vertices (d for diagonal) or edges (p for perpendiculars), and i when reflection lines path through both edges and vertices. Cyclic symmetries in the middle column are labeled as g for their central gyration orders.
  Each subgroup symmetry allows one or more degrees of freedom for irregular forms. Only the g11 subgroup has no degrees of freedom but can seen as directed edges.
caption: Symmetries of a regular hendecagon. Vertices are colored by their symmetry positions. Blue mirror lines are drawn through vertices and edge. Gyration orders are given in the center.
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