Produce your own tiling using scissors

Tiling consist to fulfill the plane using one plane figure and given some rules, of course this is not possible with any figure, a figure that can tile the plane is called a tile, there are many ways to fulfill the plane using several rules, but here we will be concerned with the geometric transformations of the plane, that is translations, rotations, symmetries and glide symmetries. It is known that there are only 17 ways (groups)to tiling the plane using these transformations, these groups are completely described, but it still remain the question how we can produce a tile for each group. In this lecture we will give a method by using a rectangle and scissors to construct a tile for each group

We will also give a demonstration of my software.

Make Tilings by using scissors

There are exactly 17 groups of tilings by using translations, rotations or symmetries. For each group a tiling can be realized by you by using a shift of paper and scissors

Here you can see how to make each one by using a shift of paper and scissors

The following tilings has been done with the collaboration of Alice Morales

Tiling using translations(R0)

Tiling using translations and central symmetry(R2)

Tiling using translations, rotations of angle a multiple of 90°(R4)

Tiling using translations, rotations of angle a multiple of 120°(R3)

Tiling using translations, rotations of angle a multiple of 60°(R6)

Tiling using translations, and glide simmetries (M0) (No axial symmetry)

Tiling using translations, axial symmetries (M1)

Tiling using translations, a family of axial symmetry and glides symmetries(of vertical axis) (M1g)

Tiling using translations, and two families of axial symmetries (M2)

Tiling using translations, central symmetries, and glide symmetries (M0R2) (no axial symmetry )