A heptagon is a 2-dimensional polygon with seven edges. The Bowers acronym for a heptagon is heg.


The main Dynkin symbol of a regular heptagon is x7o.

Structure and Sections

The regular heptagon is the simplest regular polygon that can't be constructed with a compass and straightedge. Each angle is 128+4/7 degrees.




  • Vertex radius: \frac{1}{2sin(\frac{\pi}{7})}l
  • Edge radius: \frac{1}{2tan(\frac{\pi}{7})}l


  • Vertex angle: <nath>\frac{900}{7}</math>º

Related shapes

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
t_0 \{7\}
t_1 \{7\}
t_{0,1} \{7\}
Heptagon Heptagon Tetradecagon