Tessellation
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A tessellation is created when a shape is repeated over and over again covering a
plane without any gaps or overlaps. Another word for a tessellation is a tiling.
In dictionary, the word “tessellate” means to form or arrange small squares in a
checkered or mosaic pattern. The word "tessellate" is derived from the Ionic version of the
Greek word “tesseres” which in English means “four”. The first tilings were made from
square tiles.
A regular polygon has 3 or 4 or 5 or more sides and angles, all are equal. A regular
tessellation means a tessellation made up of congruent regular polygons. Regular means that
the sides and angles of the polygon are all equivalent. Congruent means that the polygons that
put together are all the same size and shape.
Only three regular polygons tessellate in the Euclidean plane: triangles, squares or
hexagons. Here are examples of
a tessellation of triangles
a tessellation of squares
a tessellation of hexagons
When look at these three samples we can easily notice that the squares are lined up with each
other while the triangles and hexagons are not. Also, if look at 6 triangles at a time, they form
a hexagon, so the tiling of triangles and the tiling of hexagons are similar and they cannot be
formed by directly lining shapes up under each other.
Since the regular polygons in a tessellation must fill the plane at each vertex, the
interior angle must be an exact divisor of 360 degrees. This works for the triangle, square,
and hexagon. For all the others, the interior angles are not exact divisors of 360 degrees, and
therefore those figures cannot tile the plane.
Besides regular tessellation, there is a semi-regular tessellation. A semi-regular
tessellation has two properties which are it is formed by regular polygons and the
arrangement of polygons at every vertex point is identical. These are the examples of semi-
regular tessellation:
There are an infinite number of tessellations that can be made of patterns that do not
have the same combination of angles at every vertex point. There are also tessellations made
of polygons that do not share common edges and vertices.
After knew the concept of tessellation, we started to design a geometrical pattern of
our tessellation. The design started with a square. The following are the steps of tessellation’s
design.
1. First of all, decide a theme of your design. Here, the theme we use is a fish.
2. After that, construct a square on a piece of paper and cut it down.
A B
D C
3. Construct a random geometrical shape on line BC (right side of the square). Then cut
it down.
A B
D C
4. Translate the cut part to line AD (left side of the square) and glue it. Now the shape is
as below.
A B
D C
5. Construct second random geometrical shape on line AB as below and cut it.
A B
D C
6. Translate the second cut part to line DC and glue it. Now the shape is as below.
A B
D C
7. Draw a diamond as the fish eye and a triangle as fish fin at the centre of the shape
and cut them out. After done cut, the design is done. Now, you are willing to begin
tessellate.
8. Prepare a piece of A4 paper. Start to draw the shape at the corner of your paper and
trace it precisely.
9. Slide your shape so that it fits into itself like the jig-saw piece. Continue tracing and
tracing until it fills the paper.
10. You are almost done with your tessellation. Fill in the colours and use different
colours for adjacent polygons. Now, you have done it.
Difficulties:
- Dunno the meaning of tessellation.
- No time to library to search books because we were in holiday.
- After found out the meaning (internet), it was different with the meaning gave by
lecturer. Went to ask friends.
- It was quite difficult to draw the pattern of tessellation using computer because it was
troublesome.