A tessellation is an arrangement of repeating shapes that have what characteristic?

2 Answers
Jan 29, 2016

They cover the flat surface with no gaps and no overlaps.

Explanation:

Tessellation might not only consist of repeating shapes, but of any shapes, as long they cover the flat surface with overlaps and no gaps.

So, the area of a flat surface covered in tessellation is equal to a sum of areas of shapes that cover it.

May 28, 2016

We can also refer to a shape tessellating.
This means that the same shape is used again and again to cover an area completely without leaving any gaps. Sometimes it might need to be rotated or reflected.
At every vertex the sum of the angles is 360°.

All triangles tessellate, some quadrilaterals tessellate.

Regular pentagons and octagons do not tessellate, but regular hexagons do. (As in honeycomb or pavers for example.)

Circles never tessellate in 2 dimensions.