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A hexagon is a 2-dimensional polygon with six edges. The Bowers acronym for a hexagon is hig. It is one of the regular polygons that can tile 2-D space forming the hexagonal tiling, unlike pentagons, which cannot tile the plane. Hexagons have the greatest numbers of edges and angles of any regular polygon that can tile the plane.

Symbols

Dynkin symbols for the hexagon include:

  • x6o (regular)
  • x3x (ditrigon)
  • ho3oh&#zx (triambus)
  • xu ho&#zx (rectangle symmetry)
  • xux&#xt
  • ohho&#xt

Structure and Sections

The regular hexagon has equal edge lengths and each angle as 120 degrees. It can be seen as a truncated triangle.

Hypervolumes

  • vertex count = $ 6 $
  • edge length = $ 6l $
  • surface area = $ \frac{3\sqrt{3}}{2} {l}^{2} $

Subfacets

Radii

  • Vertex radius: $ l $
  • Edge radius: $ \frac{\sqrt{3}}{2}l $

Angles

  • Vertex angle: 120º

Vertex coordinates

The vertex coordinates of a regular hexagon of side 2 are:

  • (±1,±√3)
  • (±2,0)

Related shapes

  • Dual: Self dual
  • Vertex figure: Line segment, length $ \sqrt{3} $

See Also

$ \{1\} $ $ \{2\} $ $ \{3\} $ $ \{4\} $ $ \{5\} $ $ \{\frac{5}{2}\} $ $ \{6\} $ $ \{7\} $ $ \{\frac{7}{2}\} $ $ \{\frac{7}{3}\} $ $ \{8\} $ $ \{\frac{8}{3}\} $ $ \{9\} $ $ \{\frac{9}{2}\} $ $ \{\frac{9}{4}\} $ $ \{10\} $ $ \{\frac{10}{3}\} $ $ \{11\} $ $ \{\frac{11}{2}\} $ $ \{\frac{11}{3}\} $ $ \{\frac{11}{4}\} $ $ \{\frac{11}{5}\} $ $ \{12\} $ $ \{\frac{12}{5}\} $ $ \{13\} $ $ \{\frac{13}{2}\} $ $ \{\frac{13}{3}\} $ $ \{\frac{13}{4}\} $ $ \{\frac{13}{5}\} $ $ \{\frac{13}{6}\} $ $ \{14\} $ $ \{\frac{14}{3}\} $ $ \{\frac{14}{5}\} $ $ \{15\} $ $ \{\frac{15}{2}\} $ $ \{\frac{15}{4}\} $ $ \{\frac{15}{7}\} $ $ \{16\} $ $ \{\frac{16}{3}\} $ $ \{\frac{16}{5}\} $ $ \{\frac{16}{7}\} $ ... $ \{\infty\} $ $ \{x\} $ $ \{\frac{\pi i}{\lambda}\} $
Monogon Digon Triangle Square Pentagon Pentagram Hexagon Heptagon Heptagram Great heptagram Octagon Octagram Enneagon Enneagram Great enneagram Decagon Decagram Hendecagon Small hendecagram Hendecagram Great hendecagram Grand hendecagram Dodecagon Dodecagram Tridecagon Small tridecagram Tridecagram Medial tridecagram Great tridecagram Grand tridecagram Tetradecagon Tetradecagram Great tetradecagram Pentadecagon Small pentadecagram Pentadecagram Great pentadecagram Hexadecagon Small hexadecagram Hexadecagram Great hexadecagram ... Apeirogon Apeirogram ($ x $-gon) Pseudogon ($ \frac{\pi i}{\lambda} $-gon)
Regular
$ t_0 \{6\} $
Rectified
$ t_1 \{6\} $
Truncated
$ t_{0,1} \{6\} $
Hexagon Hexagon Dodecagon
Regular
$ t_0 \{3\} $
Rectified
$ t_1 \{3\} $
Truncated
$ t_{0,1} \{3\} $
Triangle Triangle Hexagon
Regular
$ t_0 \{\frac{6}{5} \} $
Rectified
$ t_1 \{\frac{6}{5} \} $
Truncated
$ t_{0,1} \{\frac{6}{5} \} $
Hexagon Hexagon Dodecagram