# Tessellation

**Topics:**Tessellation, Hexagon, Regular polygon

**Pages:**2 (428 words)

**Published:**May 2, 2013

| By: Lee Pak Long8B23|

By: 8B (23) Lee Pak Long

So, what is “Tessellation? According to the dictionary, Tessellation is the process of creating a pattern using the repetition of a shape with no overlaps and no gaps at all, which the word “tessellate” comes from the Greek word “Tesseres” ,which means “4”.

Otherwise, comprehending in a simpler manner, a way to tile a floor. Also, the puzzle you did last time is also a tessellation actually. Since primary school, we have learnt about 2D tessellation, which can also be found in our mother nature. When basaltic lava flows they mostly have cracks on them caused by contraction forces, creating columns of harden lava which resembles the tessellation of regular hexagons. One of the most famous example, the Giant’s Causeway in Northern Ireland. Tessellations can also found in daily life. For example, the tilings on the floor, toilets etc. For regular tessellation mentioned before, there are actually only 3 types of regular polygons which can be tessellated by themselves, which is : 1. Triangles

2. Squares

3. Hexagons

Only three regular tessellations exist, because there are only three polygons whose interior angles divide evenly into 360 degrees: the triangle (60 degrees) the square (90 degrees) and the hexagon (120 degrees). Of the regular polygons, only triangles, squares, hexagons, octagons, and dodecagons can be used for tiling around a common vertex - again because of the angle value, and 14 such combinations exist! The combination is :

Combination of Polygons| Combination of Angles|

6 triangles| 6X 60 = 360|

4 squares| 4 X 90 = 360|

3 hexagons| 3 X 120 = 360|

3 triangles and 2 squares| (3 X 60) + (2 X 90) = 360|

3 triangles and 2 squares - another formation| (3 X 60) + (2 X 90) = 360| 2 hexagons and 2 triangles| (2 X 120) + (2 X 60) = 360|

2 hexagons and 2 triangles - another formation| (2 X 120) + (2 X 60) = 360| 1 hexagon, 2 squares,...

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