![octagon tessellation octagon tessellation](https://1.bp.blogspot.com/-7DpDmQYI12w/T70Z3dI3JuI/AAAAAAAAE8Q/0Vs_rrVcZyM/s1600/bigoctsq+-+Copy.gif)
Each vertex looks the same – two triangles and two hexagonsĨ. Each vertex looks the same – three triangles and two squares:ħ. Each vertex looks the same – one square and two octagons:Ħ. Each vertex looks the same – three triangles and two squares:ĥ. Each vertex looks the same – one square, one hexagon and one dodecagon:Ĥ. Each vertex looks the same – one triangle and two dodecagons:ģ. Each vertex looks the same – four triangles and one hexagon:Ģ. There are only 8 combinations of different regular polygons that create semi-regular tessellations.ġ. Even more precisely, each vertex has the same pattern of polygons around it. Just like regular tessellations, every vertex looks the same and the sum of the interior angles at each vertex is 360°. Semi-Regular tessellations are composed of 2 or more different regular polygons. Try it for yourself using the equation (n – 2) x 180° / n. They will all overlap and therefore, will not tessellate. Neither do octagons (405), or nonagons (420), or decagons (432) or in fact, any regular polygon with more than six sides. The interior angle of a hexagon is 120 degrees. Yay! Each vertex looks the same – has the exact same composition of shapes around it: three hexagons.
![octagon tessellation octagon tessellation](https://robertlovespi.files.wordpress.com/2018/09/tessellation-of-star-octagons-and-two-sizes-of-squares.png)
The interior angle of a pentagon is 108 degrees. Oh no! We have a gap between the pentagons! The interior angle of a square is 90 degrees. The interior angle of an equilateral triangle is 60 degrees.Įach vertex looks the same – has the exact same composition of shapes around it: four squares. Notice that each vertex looks the same – has the exact same composition of shapes around it: six triangles. Let’s go through some regular polygons one by one to see why only three work and the others don’t. Only three combinations of singular regular polygons create regular tessellations. Every vertex looks the same and the sum of the interior angles at each vertex is 360°. Regular tessellations are made up entirely of identically sized and shaped regular polygons. Now that we have a better understanding of some basic geometry, let’s move onto the classification of tessellations of which there are three: regular, semi-regular and non-regular. The interior angle at any vertex of a regular polygon is (n – 2) x 180° / n.Įxterior angle – an angle outside a polygon at one of its vertices. The sum of the interior angles of a regular polygon is (n – 2) x 180° where n is the number of sides of the polygon. Interior angle – an angle inside a polygon at one of its vertices. Vertex – a point where two lines meet to form an angle. Regular polygon – a polygon whose sides are all the same length (equilateral) and whose angles are all the same (equiangular) otherwise, it is an Irregular Polygon. Simple Polygon – any two-dimensional shape formed with straight lines that do not intersect and and is closed. Semi-regular tessellations are made up with two or more types of regular polygon which are fitted together in such a way that the same polygons in the same cyclic order surround every vertex.To better understand TESSELLATIONS, let’s review some GEOMETRY! #color(brown)("What are different types of tessellation?"# There are only three regular tessellations which use a network of equilateral triangles, squares and hexagons.
![octagon tessellation octagon tessellation](https://live.staticflickr.com/7401/12850775635_eb08970b8d_n.jpg)
You can have other tessellations of regular shapes if you use more than one type of shape. Triangles, squares and hexagons are the only regular shapes which tessellate by themselves. #color(brown)("What shapes tessellate and why?"# In mathematics, tessellations can be generalised to higher dimensions and a variety of geometries.Ī tiling that lacks a repeating pattern is called "non-periodic". #color(brown)("What does it mean for a shape to tessellate?"#Ī tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.