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In the triangle pattern, 6 triangles meet at every vertex (corner). So, angle = 6 × 60° = 360° (so, there

is no gap).
In the square pattern, 4 squares meet at every vertex.

So, angle = 4 × 90° = 360° (so, there is no gap).

In the hexagon pattern, at every vertex three hexagons meet.

So, angle = 3 × 120° = 360° (so, there is no gap).

Now, look at the following tilling patterns.

Here, in the first tilling pattern every vertex is surrounded by a triangle, a hexagon, a triangle and
a hexagon. What do you observe in the second tilling pattern given above?
By using two or more regular polygons, we can make semi-regular patterns of tiling.

Some more semi-regular tilling patterns are shown below.

A basic tiling, such as regular or semi-regular tiling, can be modified to make a tiling that uses

more complex shapes. To do so, we can carefully modify the edges of the tiles by cutting pieces
from one side and pasting them on the other side wherever required.

Below is an example of “slanted checkerboard” tiling of parallelograms which has been modified
by cutting a notch from the left-hand side and adding a triangular point to the right-hand side so
that the tiles will fit together.

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