0
A regular polygon's angles are measured by the formula 180 * (n - 2) / n.
Regular polygons will only tesselate if m * ( 180 * (n - 2) / n ) = 360, where m is an integer.
Let's go through all the possible regular polygons.
3 sided polygon: m * ( 180 * 1 / 3 ) = 360 -> 60m=360 -> m=6, Able to tesselate
4 sided polygon: m * ( 180 * 2 / 4 ) = 360 -> 90m=360 -> m=4, Able to tesselate
5 sided polygon: m * ( 180 * 3 / 5 ) = 360 -> 108m=360. Not able to tesselate
6 sided: m * ( 180 * 4 / 6 ) = 360 -> 120m=360. Able to tesselate
We do not need to check more, for the polygons that are able to tesselate have a decreasing m value, from 6 to 4 to 3. The next possible m value would be 2, and we know this cannot happen, because if m = 2, then the polygon would have to have angles of 180 degrees; impossible.
Therefore, we can only tesselate using triangles, squares, and hexagons.
Add your answer:
Earn +20 pts
What is the number of polygon sides can be used for tesselations?
For regular polygons: 3, 4, or 6. For irregular polygons, figures with any number of sides can be found.
Can a semi-regular tessellation be made from octagons and rhombi?
Strictly speaking, no, because a semi-regular tessellation must be based on regular polygons and rhombi are not regular polygons. However, octagons and rhombi can be used to make a non-regular tessellation.
What is used to create a regular tessellation?
The only shapes which can be used for a regular tessellation are:An equilateral triangle,A squareA regular hexagon.There are also non-regular polygons as well as shapes which are not polygons which can tessellate
Is circle regular or irregular?
Regular, although the term is more usually used with polygons and polyhedra.
Which one of the following sets of regular polygons can be used for a semiregular tessellation?
See the answer below.
What is the number of polygon sides can be used for tesselations?
For regular polygons: 3, 4, or 6. For irregular polygons, figures with any number of sides can be found.
Can a semi-regular tessellation be made from octagons and rhombi?
Strictly speaking, no, because a semi-regular tessellation must be based on regular polygons and rhombi are not regular polygons. However, octagons and rhombi can be used to make a non-regular tessellation.
Which regular polygon can be used by itself to make a tessellation?
The only regular polygons are those with 3, 4 or 6 sides.
What polygons can be used to make tessellations?
Regular tessellations can be made using triangles, squares, and hexagons.
What is used to create a regular tessellation?
The only shapes which can be used for a regular tessellation are:An equilateral triangle,A squareA regular hexagon.There are also non-regular polygons as well as shapes which are not polygons which can tessellate
What does semi regular tessellation have?
It has two regular polygons which can be used together to tessellate a plane.
Is circle regular or irregular?
Regular, although the term is more usually used with polygons and polyhedra.
Is a circle a regular or a irregular shape?
The terms "regular" and "irregular" are used for polygons, not for just any shape.
Which shapes have all sides equal?
All regular polygons. But there are also others which look like squashed versions of regular polygons. A "squashed" square makes a rhombus. Similarly there are squashed polygons with larger numbers of sides. They should be called equilateral polygons, but that phrase is not much used.
Which one of the following sets of regular polygons can be used for a semiregular tessellation?
See the answer below.
How do you classify the polygons that are used to create each tessellation?
There are regular polygons (with 3, 4 and 6 sides).There are irregular convex polygons (with 3, 4, 5 or 6 sides). There are [irregular] concave polygons with various numbers of sides.
Which polygons cannot be used to form a regular tesselation?
Most regular polygons will not tessellate but if their interior angles is a factor of 360 degrees then they will tessellate or if their angles around a point add up to 360 degrees then they also will tessellate.
