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A dodecagon is a 2-dimensional polygon with twelve edges. The Bowers acronym for a dodecagon is dog.

Structure and Sections

The regular dodecagon has each angle at 150 degrees. It can be seen as a truncated hexagon.

Hypervolumes

  • vertex count = $ 12 $
  • edge length = $ 12l $
  • surface area = $ 3\left(2 + \sqrt{3}\right) l^2 $

Subfacets

Radii

  • Vertex radius: $ \frac{\sqrt{2}+\sqrt{6}}{2}l $
  • Edge radius: $ \frac{2+\sqrt{3}}{2}l $

Angles

  • Vertex angle: 150º

Vertex coordinates

The vertices of a regular dodecagon centered at the origin, of side 2, can be given by all sign changes of:

  • (1+√3, 1+√3)
  • (1, 2+√3)
  • (2+√3, 1)

Related shapes

  • Dual: Self-dual
  • Vertex figure (and second diagonal): Line segment, length $ \frac{\sqrt{2}+\sqrt{6}}{2} $
  • Third diagonal: [[Length $ 1+\sqrt{3} $
  • Fourth diagonal: Length $ \frac{3\sqrt{2}+\sqrt{6}}{2} $
  • Fifth diagonal: Length $ 2+\sqrt{3} $
  • Longest diagonal: Length $ \sqrt{2}+\sqrt{6} $

See Also

$ \{0\} $ $ \{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}\} $
Zerogon 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 Failed star polygon ($ x $-gon) Pseudogon ($ \frac{\pi i}{\lambda} $-gon)
Regular
$ t_0 \{12\} $
Rectified
$ t_1 \{12\} $
Truncated
$ t_{0,1} \{12\} $
Dodecagon Dodecagon Icositetragon
Regular
$ t_0 \{6\} $
Rectified
$ t_1 \{6\} $
Truncated
$ t_{0,1} \{6\} $
Hexagon Hexagon Dodecagon
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