Octadecagon

[2] 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.

Coxeter states that every zonogon (a 2m-gon whose opposite sides are parallel and of equal length) can be dissected into m(m-1)/2 parallelograms.

[6] In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi.

The list OEIS: A006245 enumerates the number of solutions as 112018190, including up to 18-fold rotations and chiral forms in reflection.

[7] However, this pattern cannot be extended to an Archimedean tiling of the plane: because the triangle and the nonagon both have an odd number of sides, neither of them can be completely surrounded by a ring alternating the other two kinds of polygon.

Deeper truncations of the regular enneagon and enneagrams can produce isogonal (vertex-transitive) intermediate octadecagram forms with equally spaced vertices and two edge lengths.

Octadecagon with all 135 diagonals
Octadecagon, an exact construction based on the angle trisection 120° by means of the tomahawk, animation 1 min 34 s.
Symmetries of a regular octadecagon. Vertices are colored by their symmetry positions. Blue mirrors are drawn through vertices, and purple mirrors are drawn through edge. Gyration orders are given in the center.
18-gon with 144 rhombs
An equilateral pentagonal dissection , with sequential internal angles: 60°, 160°, 80°, 100°, and 140°. Each of the 24 pentagons can be seen as the union of an equilateral triangle and an 80° rhombus . [ 5 ]