Octadecagon Octadecagon An octadecagon (or octakaidecagon) or 18-gon is an eighteen-sided polygon. A "regular octadecagon" has a Schläfli symbol {18} and can be constructed as a quasiregular truncated enneagon, t{9}, which alternates two types of edges. As 18 = 2 × 3, a regular octadecagon cannot be constructed using a compass and straightedge. However, it is constructible using neusis, or an angle trisection with a tomahawk. The following approximate construction is very similar to that of the enneagon, as an octadecagon can be constructed as a truncated enneagon. It is also feasible with exclusive use of compass and straightedge. The "regular
Octadecagon octadecagon" has Dih symmetry, order 36. There are 5 subgroup dihedral symmetries: Dih, (Dih, Dih), and (Dih Dih), and 6 cyclic group symmetries: (Z, Z), (Z, Z), and (Z, Z). These 15 symmetries can be seen in 12 distinct symmetries on the octadecagon. John Conway labels these by a letter and group order. Full symmetry of the regular form is r36 and no symmetry is labeled a1. The dihedral symmetries are divided depending on whether they pass through vertices (d for diagonal) or edges (p for perpendiculars), and i when reflection lines path through both edges and vertices. Cyclic symmetries