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When a regular polygon can tessellate, it can be placed around a point (which has an angle of 360 degrees) with no 'space' left over. However some regular polygons don't tessellate because their interior angle is not a factor of 360 (does not go into 360 equally), meaning that there will be 'space' left over or it will overlap. To check if a regular polygon can tessellate, see if it's interior angle goes into 360 equally. (360/interior angle), if it does, it will tessellate and if it doesn't it's because the interior angle is not a factor of 360 meaning it will not fit round a point and won't tessellate.
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Does an even numbered sided shape tessellate?
Some do, some don't. For regular tessellation, you require the interior angles to be a factor of 360 degrees. An octagon will not tessellate. On the other hand a triangle, which does not have an even number of sides, will.
Is it possible to tile a floor with copies of a regular polygon?
Yes, but only with some polygons.
Is it true you can not tessellate six sides polygon by itself?
No, it is not true that you cannot tessellate a six-sided polygon by itself. Hexagons are a type of polygon that can tessellate, which means they can be arranged in a repeating pattern to completely cover a plane without any gaps or overlaps.
Why can only some shapes tessellate?
Shapes can tessellate only if a number of them can meet at a point and cover 360 degrees without overlap. For regular shapes this requires that the angles of the shape are a factor of 360 degrees. For non-regular shapes it is necessary that the angles of the shapes can be grouped so that they sum to 360 degrees.
How 3D shape tessellate?
Some 3D shapes will tessellate as for example a brick wall
What shapes do not tessellate?
Shapes such as circles, regular pentagons, and heptagons.Most regular polygons will not tessellate on their own. Only triangles, squares and hexagons will.With irregular polygons there is more of a choice. All isosceles or scalene triangles, parallelograms, trapeziums and kites will tessellate as will some higher order polygons.
Can irregular polygons tessellate?
Some can, but not all. For example, rhombi, rhomboids, oblongs, and isosceles triangles can tessellate; however, most irregular polygons cannot. * * * * * True, but an incomplete answer. All triangles and quadrilaterals, whether regular or irregular, will tessellate. No regular pentagon will tessellate but (as of 2016), there are 15 irregular pentagons which will tessellate. There are 3 convex hexagons, (regular and 2 irregular) which will tessellate. No polygon with 7 or more sides, even if it is regular, will tessellate.
How do you classify a polygon in a tessellation?
Some polygons will tessellate,some with tessellate along with one or more other polygons,some will not tessellate.These classes have no specific names.
Can a hexagon be tessellated?
A regular hexagon and some irregular ones will tessellate, But in general they will not.
Can some one give me a haiku about polygons?
Shapes with many sides, Polygons tessellate well, Geometry fun.
What is the secret that allows some regular polygon to tessellate and not others?
If their exterior angles are factors of 360 then they will tessellate.
What polygon can be tessellate?
Regular polygons: Equilateral triangles, squares, rectangles, rhombi, hexagons. Irregular polygons: Isosceles triangles and symmetric trapeziums (isosceles triangles with the odd angle cut off by a line parallel to the base) will do if they are alternating up and down. There are also many irregular shapes. MC Escher (see for example, http:/www.mcescher.com/Gallery/gallery-symmetry.htm) used repeated irregular shapes to tessellate. Although some of these have curved sides, they can be replaced by appropriate straight sides to produce polygons which will do the trick.
What are some real life examples of regular polygons?
A beehive.
Is there a relationship between angles and tesselations?
Yes, eg only regular polygons with an internal angle which divides evenly into 360 and only some of them, can tessellate the plane: Triangles (60), Squares (90) and Hexagons (120). Octagons (45) and Dodecagons (30) can't.
What are the names of polygons which are equilateral but not regular?
They would be equilateral concave polygons. See the related link to see some diagrams.
Does an even numbered sided shape tessellate?
Some do, some don't. For regular tessellation, you require the interior angles to be a factor of 360 degrees. An octagon will not tessellate. On the other hand a triangle, which does not have an even number of sides, will.
Is it possible to tile a floor with copies of a regular polygon?
Yes, but only with some polygons.
