Octagon

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

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

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.