Aventails are curtains of chainmail attached to a helmet. The mail is not covering the top of the head. The connection of the mail and the helmet can be made directly with rings linking into holes in the plate. Yet it is more elegant with the help of a leather band and some. In this example for a 14th-century bascinet, the aventail can be removed by pulling out the bright leather strap.
An aventail is constructed much like a coif with a round brim. There is a consistent amount of expansions located below the chin and all around the neck. The expansions are best arranged at a regular distance from each other. An average amount of 8 expansions per row is good to widen the aventail adequately. That is still the case when some rows hold no expansions and others hold more.
In the Lyle-Bascinet there are 24 expansions in one row followed by two rows void of expansions. 24/3=8 expansions per row. The expansion are highlighted for you with color. Each colored dot is a ring that only links to three others. Rings in blue are sticking out of the mesh clockwise and rings in red counter-clockwise. This is a remarkable particularity, yet not necessary to achieve the general shape.
To assemble an aventail like this, one way is to create tapering segments and connect them. Then the expansions will be created along the seams. A second way is to grow the mail row by row and build in expansions as you go. It helps to mark the expansions to keep an overview.
The finished piece of mail can be sewn onto a textile padding to tame its movement. Often rings for the aventail are chosen heavier and sturdier than one would expect on other body parts. This helps protect the vulnerable neck area.
Understand what expansions and contractions are.
Read about Mail Coifs.