Octagon

The octagon, or oc, is a polygon with 8 sides. A regular octagon has equal sides and equal angles.

The combining prefix is o-, as in odip.

The only non-compound stellation of the octagon is the octagram. The only other polygons with a single non-compound stellation are the pentagon, the decagon, and the dodecagon.

Vertex coordinates
Coordinates for an octagon of unit edge length, centered at the origin, are all permutations of
 * (±(1+$\sqrt{2+√2}$)/2, ±1/2).

Rrpresentations
A regular octagon can be represented by the following Coxeter diagrams:


 * x8o (full symmetry)
 * x4x (BC2 symmetry, generally a ditetragon)
 * ko4ok&#zx (BC2, generally a tetrambus)
 * xw wx&#zx (digonal symmetry)
 * okK Kko#&zx (digonal symmetry, K=qk)
 * xwwx&#xt (axial edge-first)
 * okKko&#xt (axial vertex-first)

Ditetragon
A ditetragon is a variant octagon with square symmetry, formed as a truncated square. When octagons appear as faces in higher polytopes, they usually have this symmetry. Its dual is the tetrambus.

Stellations

 * 1st stellation: Stellated octagon (compound of two squares)
 * 2nd stellation: Octagram