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In a tessellation a number of polygons meet at a point. If n polygons meet, then there will be n vertices. These must add up to 360 degrees so that the tessellation does not leave holes. So the interior angles of the polygon must be a factor of 360 degrees.
Interior angle of an equilateral triangle = 60 deg = 360/6 and so it will tessellate;
Interior angle of a square = 90 deg = 360/4 and so it will tessellate;
Interior angle of a regular pentagon = 108 deg which is not a factor of 360 and so it will not tessellate;
etc.
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What regular polygons have rotational symmetry?
All of them have rotational symmetry because all the sides and angles have to be the same in order for the polygon to be a regular polygon
What shape has a rotational symmetry of 120 degree?
An equilateral triangle, and all regular polygons with 3n sides.
How do you work out the sum of exterior angles for a pentagon?
all regular polygons (such as a pentagon) have the sum of their exterior angles = 360 degrees
What is the measure of an exterior angle of a regular polygon with 8 sides?
All polygons exterior angles sum to 360. If it is regular it means all angles are equal So all 8 angles are the same number 8x = 360 x = 45 Each angle is 45 degrees
Is a pentagon a regular polygon sometimes always or never?
All polygons can be irregular sense the requirements for a polygon to be irregular is for 1 or more sides to be unequal to the others. So a pentagon is sometimes a regular polygon. Hope that answers your question.
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.
What are all the shapes that tessellate with themselfs?
All regular polygons whose interior angles are a factor of 360 degrees will tessellate with themselves
Why do shapes tessellate?
Shapes tessellate to fit around an interior angle. They also tessellate because they are regular polygons; non-regular polygons cannot tessellate. * * * * * Not correct. All triangles and quadrilaterals will tessellate, whether regular or irregular. Contrary to the above answer, a regular pentagon will not tessellate but there are 14 different irregular pentagons which will tessellate (the last was discovered in 2015). Three convex hexagons will do so as well. No polygon of 7 or more sides will tessellate - whether they are regular (contrary to the above answer) or irregular.
Is it possible to create a regular tesselation with a regular polygon?
Certain polygons, yes. Squares, Triangles and Hexagons are all shapes which, in their regular form, can tessellate. Other polygons cannot.
Will all polygons tessellate?
No because only polygons whose interior angles are a factor of 360 will tessellate. For instance a regular pentagon will not tessellate because its interior angle is 108 degrees but a hexagon will tessellate because its interior angle is 120 degrees which is a factor of 360.
Can all regular polygons tessellate?
No only three can tesselate. they are: An equilateral triangle, a square and a 6 sided hexagon.
What polygons were used to make the tessellation?
All triangles will tessellate. All quadrilaterals will tessellate There are 15 classes of convex pentagons (the latest discovered in 2015) which will tessellate. Regular hexagons will tessellate. In addition, there are 3 classes of irregular convex hexagons which will tessellate. No convex polygon with 7 or more sides will tessellate.
Which of the polygons cannot be used to create a pure tessellation?
The only regular polygons which will tessellate are those with 3, 4 or 6 sides. But all irregular triangles, all irregular quadrilaterals, 15 classes of irregular convex pentagons and 3 classes of irregular convex hexagons will tessellate. In addition, there are concave polygons with different numbers of sides which will also tessellate.
Will a 15-gon tessellate?
No To find out if a regular polygon tessellates you have to do A=180(sides-2) all over 2. Then you do 360/answer and if it is a whole number it does tessellate. * * * * * Correct answer but the reasoning is limited to regular polygons. According to that logic, a pentagon should not tessellate. But there are 15 pentagons (all irregular) which will.
How can you determine whether given shapes will make a tessellation?
There is no simple way.All triangles will tessellate. All quadrilaterals will tessellate There are 15 classes of convex pentagons (the latest discovered in 2015) which will tessellate. Regular hexagons will tessellate. In addition, there are 3 classes of irregular convex hexagons which will tessellate. No convex polygon with 7 or more sides will tessellate.In addition, there are concave polygons, and non-polygons which will tessellate.
Does a decagon tesselate?
yes of course * * * * * A decagon does NOT tessellate. All triangles and quadrilaterals do, there are 14 tessellating pentagons and a number of hexagons (including regular hexagons). There are no tessellations which use polygons of the same shape - regular or irregular - for polygons with 7 or more sides.
