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An octagon is a 2-dimensional polygon with eight edges. The Bowers acronym for an octagon is oc.

## Symbols

Symbols for the octagon include:

• x8o (regular)
• x4x (ditetragon)
• ko4ok&#zx (tetrambus)
• xwwx&#zx (edge first)
• xw wx&#zx (rectangle symmetry)

## Structure and Sections

The regular octagon has each angle at 135 degrees. It can be seen as a truncated square.

### Subfacets

• Vertex radius: $\sqrt{\frac{2+\sqrt{2}}{2}}l$
• edge radius; $\frac{1+\sqrt{2}}{2}l$

### Angles

• Vertex angle: 135º

### Vertex coordinates

The coordinates of a regular octagon are all permutations and sign changes of (1,1+√2).

### Related shapes

• Dual: Self-dual
• Vertex figure: Line segment, length $\sqrt{2+\sqrt{2}}$

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