Geometry and Spatial Sense: Tesselations

Tesselation: the repetition of a pattern that covers an entire region--it is important that part being repeated must fit together with itself.

The following illustrates the construction of one tesselation. Examples below demonstrate other methods for constructing tesselations. In each case forming the initial element to be repeated is important. Uses of additive and subtractive principles maintain equivalent spaces so that the initial element will fit with itself for repetition.

1. Figure T1 shows starting with a square.
   

   Figure T1

2. Figure T2 reveals the locating of the midpoint on the top of the square.
   

   Figure T2

3. Figure T3 illustrates forming a circle with the upper left vertex and the midpoint on the top of the square.
   

   Figure T3

4. Equivalent areas can be added and subtracted as in Figure T4. The semicircle added at the top. A copy of the semicirlcle is rotated about the midpoint in Figure T4.

   

   Figure T4

5. Figure T5 demonstrates copy of the transformations at the top translated to the bottom of the square.

   

   Figure T5

6. The above should be repeated to form tiles. See Full Tesselation

Additional Tesselations:

• Tiling or Tesselation #1
• Tessellation #2
• Sample Pattern Block Pattern or Tesselation #3
• Sample Triangle Tesselation #4
• HyperStudio Tesselation #5

| Symmetry | Reflection/Flip | Translation/Slide | Rotation/Turn | TanTrans | Congruency | Dilation/Scaling | Similarity | Tesselations | Perpendicularity | Parallelism |

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