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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

Regular polygons $ \{1\} $ $ \{2\} $ $ \{3\} $ $ \{4\} $ $ \{5\} $ $ \{6\} $ $ \{7\} $ $ \{8\} $ $ \{9\} $ $ \{10\} $ $ \{11\} $ $ \{12\} $ $ \{13\} $ $ \{14\} $ $ \{15\} $ $ \{16\} $ ... $ \{\aleph_0\} $
$ \{\frac{n}{1}\} $ Monogon Digon Triangle Square Pentagon Hexagon Heptagon Octagon Enneagon Decagon Hendecagon Dodecagon Tridecagon Tetradecagon Pentadecagon Hexadecagon ... Apeirogon
$ \{\frac{n}{2}\} $ N/A N/A Triangle (retrograde) Degenerate Pentagram Degenerate Heptagram Degenerate Enneagram Degenerate Small hendecagram Degenerate Small tridecagram Degenerate Small pentadecagram Degenerate ... N/A
$ \{\frac{n}{3}\} $ N/A N/A N/A Square (retrograde) Pentagram (retrograde) Degenerate Great heptagram Octagram Degenerate Decagram Hendecagram Degenerate Tridecagram Tetradecagram Degenerate Small hexadecagram ... N/A
$ \{\frac{n}{4}\} $ N/A N/A N/A N/A Pentagon (retrograde) Degenerate Great heptagram (retrograde) Degenerate Great enneagram Degenerate Great hendecagram Degenerate Medial tridecagram Degenerate Pentadecagram Degenerate ... N/A
$ \{\frac{n}{5}\} $ N/A N/A N/A N/A N/A Hexagon (retrograde) Heptagram (retrograde) Octagram (retrograde) Great enneagram (retrograde) Degenerate Grand hendecagram Dodecagram Great tridecagram Great tetradecagram Degenerate Hexadecagram ... N/A
$ \{\frac{n}{6}\} $ N/A N/A N/A N/A N/A N/A Heptagon (retrograde) Degenerate Degenerate Degenerate Grand hendecagram (retrograde) Degenerate Grand tridecagram Degenerate Degenerate Degenerate ... N/A
$ \{\frac{n}{7}\} $ N/A N/A N/A N/A N/A N/A N/A Octagon (retrograde) Enneagram (retrograde) Decagram (retrograde) Great hendecagram (retrograde) Dodecagram (retrograde) Grand tridecagram (retrograde) Degenerate Great pentadecagram Great hexadecagram ... N/A
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