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What regular polygons can be used to make a regular tesselations?
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.
Can you tesselate a regular octagon?
No, you cannot.
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.
Does a regular 20 sided polygon tesselate?
No
Can a pentagonal prism tesselate?
Yes. Can it tesselate R^3? Only if its base pentagon is non-regular.
Which regular polygons will tesselate?
Triangle, square, hexagon.
You cannot tesselate eight sided regular polygons by themselves?
True
Can all regular polygons tessellate?
No only three can tesselate. they are: An equilateral triangle, a square and a 6 sided hexagon.
What regular polygons can be used to make a regular tesselations?
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.
Can a regular heptagon tesselate itself?
No.
Can you tesselate a regular octagon?
No, you cannot.
Can a regular heptagon tesselate?
No, it cannot.
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.
What types of figures tessellations the plane?
All sorts of figures. The only regular polygons that can tessellate by themselves are triangles, squares and hexagons. Irregular polygons such as rectangles, rhombuses, parallelograms and trapeziums will as well. Regular octagons combined with squares will. Other regular polygons can be combined with appropriate star-shapes to tesselate. There are also Penrose tilings which, although they cover the plane, are non-periodic in the sense that the pattern does not repeat itself if you move along. Finally there are many irregular shapes that will tessellate.
Does a regular hexagon tesselate?
Yes, a regular hexagon does tessellate.
Does a regular 20 sided polygon tesselate?
No
Can a pentagonal prism tesselate?
Yes. Can it tesselate R^3? Only if its base pentagon is non-regular.
