Tessellations by Convex Polygons. Every shape of triangle can be used to tessellate the plane. Every shape of quadrilateral can be used to tessellate the plane. Since triangles have angle sum 180° and quadrilaterals have angle sum 360°, copies of one tile can fill out the 360° surrounding a vertex of the tessellation.

No, a regular octagon cannot tessellate.

Turtle shells, honeycombs, raspberries, quilts, fish scales and the art of M.C. Escher are just a few examples of real-life tessellations. Tessellations are patterns that repeat over and over without overlapping or leaving any gaps. Additional examples are snake skins, pineapples, origami and tile floors.

Art, architecture, hobbies, and many other areas hold examples of tessellations found in our everyday surroundings. Specific examples include oriental carpets, quilts, origami, Islamic architecture, and the are of M. C. Escher. Oriental carpets hold tessellations indirectly.

The brick wall provides a tessellation with rectangles and the honeycomb is a tessellation of regular hexagons. These tessellations provide a strong structure for their two different purposes. The key features of tessellations are that there are no gaps or overlaps.

Tessellated shapes are 2D shapes which fit exactly together, through the shapes do not have to be the same. However, you can also use mixed shapes to create tessellating patterns, such as triangles and hexagons or triangles and squares.