How to Generate Squame

To generate a Squame Module the first thing to do is decide for an angle to apply.
Let's say for instance that Alpha would be 30°.
Now draw a line: it is a side for your module.
Draw a second line of the same lenght but rotated of Alpha degrees:

Keep drawing lines, always rotating by Alpha degrees, until you reach the total limit of 180°.
Each step you have just drawed it is a pattern that can be replicated by simple translation.

Translate each pattern over the Tangent of Alpha/2 (this is the Patented Formula to generate Squame) until vertex coincide. Continue replicating all around and you will obtain a perfect tessellation for each pattern.

You have just generated 6 different Squame Modules of the 30° Family.
Right now they are standing in their simplest configuration: the Linear Tessellation,
but they are all able to curve by 30° (clockwise and counterclockwise) and keep tiling:

This means that they all can do linear, curve, radial and spiral tassellation.
And you can also combine together Squame's differents properties to make non periodic tilings and limitless free compositions.