Editing Heptagon (section)

=== Symmetry ===
[[File:Symmetries_of_heptagon.png|thumb|200px|Symmetries of a regular heptagon. Vertices are colored by their symmetry positions. Blue mirror lines are drawn through vertices and edges. Gyration orders are given in the center.<ref>John H. Conway, Heidi Burgiel, [[Chaim Goodman-Strauss]], (2008) The Symmetries of Things, {{ISBN|978-1-56881-220-5}} (Chapter 20, Generalized Schaefli symbols, Types of symmetry of a polygon pp. 275-278)</ref>]]

The ''regular heptagon'' belongs to the [[dihedral symmetry|D<sub>7h</sub>]] [[point group]] ([[Schoenflies notation]]), order 28. The symmetry elements are: a 7-fold proper rotation axis C<sub>7</sub>, a 7-fold improper rotation axis, S<sub>7</sub>, 7 vertical mirror planes, σ<sub>v</sub>, 7 2-fold rotation axes, C<sub>2</sub>, in the plane of the heptagon and a horizontal mirror plane, σ<sub>h</sub>, also in the heptagon's plane.<ref>{{cite book |last1=Salthouse |first1=J.A |url=https://books.google.com/books?id=GAw4AAAAIAAJ |title=Point group character tables and related data |last2=Ware |first2=M.J. |date=1972 |publisher=Cambridge University Press |isbn=0-521-08139-4 |location=Cambridge}}</ref> 
<!-- These 4 symmetries can be seen in 4 distinct symmetries on the heptagon. [[John Horton Conway|John Conway]] labels these by a letter and group order. Full symmetry of the regular form is '''r14''' 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 '''g7''' subgroup has no degrees of freedom but can seen as [[directed edge]]s.
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