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**

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**Produce your
own tiling using scissors**

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**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 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
)**

**Tiling using
translations, a famille de axial symmetries and
central symmetry(M1R2) **

**Tiling using
translations, two families axial symmetries and
central symmetry(M2R2) **

**Tiling using
translations, two families of axial symmetries and rotations of angle
90°(M2R4)**

**Tiling using
translations, 3 families of axial symmetries and rotations of angle
120°(M3R3)**

**Tiling using
translations, 3 families of axial symmetries (M3)**

**Tiling using
translations, four families of axial symmetries (M4)**

**Tiling using
translations, six families of axial symmetries (M6)**