There are infinitely many. For example, every different triangle can tessellate. There are 15 types of pentagons which will tessellate.
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Every triangle will tessellate and, since there are infinitely many possible triangles, there are infinitely many shapes that can be used for tessellation. On the other hand, in any single tessellation you can only use a finite number of shapes.
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Yes it is a tessellation.
A tessellation that uses more than one kind of regular polygon is called a semi-regular tessellation.
Islamic Tessellation is where all the shapes are repeated over and over again. you can find many patterns like this which are clear examples of them. although Islam forbids the drawing of figures, tessellation is another way to draw and make beautiful pictures.