Just tessellation 

         If two polygons can till the plane by their original figures, or by the transformed elements, and their repeating patterns are the same. Then we can find a economical dissection from superposing two tessellations.

{GC} to {4} (4)

Both figures can tile the plane

Tessellation element  derived from cutting and rearrangement

Complete the Tessellation

        When a polygon cannot tills the plane by it original figure, or it cannot be transformed into an element that tills the plane, we may add another polygon to till the plane. If the added polygon can also be added to the target polygon to form the tessellation and their repeating patterns were the same, then they can be dissected from superposing two tessellations. Harry Lindgren called it complete the tessellation (Frederickson, 1997).

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Adding a polygon to form  tessellation elements

Added polygon cannot fit in the target polygon

Adding irregular polygon to form tessellation element 

Polyhedral tessellation

       Sometime the element of a polygon cannot tile the plane, but it still worked well if it can tile the surfaces of a 3-dimensional polyhedron whose faces are of the target polygons. 

Till an Octahedron

Till a Cube

Till a Dodecahedrgon