## FANDOM

1,035 Pages

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

## Symbols

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.

### Subfacets

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

### Angles

• Vertex angle: $\frac{900}{7}$°

### Related shapes

• Vertex figure: Line segment, length$2\cos(\frac{\pi}{7})$
• Dual: Self-dual

$\{1\}$ $\{2\}$ $\{3\}$ $\{4\}$ $\{5\}$ $\{\frac{5}{2}\}$ $\{6\}$ $\{7\}$ $\{\frac{7}{2}\}$ $\{\frac{7}{3}\}$ $\{8\}$ $\{\frac{8}{3}\}$ $\{9\}$ $\{\frac{9}{2}\}$ $\{\frac{9}{4}\}$ $\{10\}$ $\{\frac{10}{3}\}$ $\{11\}$ $\{\frac{11}{2}\}$ $\{\frac{11}{3}\}$ $\{\frac{11}{4}\}$ $\{\frac{11}{5}\}$ $\{12\}$ $\{\frac{12}{5}\}$ $\{13\}$ $\{\frac{13}{2}\}$ $\{\frac{13}{3}\}$ $\{\frac{13}{4}\}$ $\{\frac{13}{5}\}$ $\{\frac{13}{6}\}$ $\{14\}$ $\{\frac{14}{3}\}$ $\{\frac{14}{5}\}$ $\{15\}$ $\{\frac{15}{2}\}$ $\{\frac{15}{4}\}$ $\{\frac{15}{7}\}$ $\{16\}$ $\{\frac{16}{3}\}$ $\{\frac{16}{5}\}$ $\{\frac{16}{7}\}$ ... $\{\infty\}$ $\{x\}$ $\{\frac{\pi i}{\lambda}\}$
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
$t_0 \{7\}$
Rectified
$t_1 \{7\}$
Truncated
$t_{0,1} \{7\}$