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What regular polygons tessellate by themselves?
Triangles, squares and hexagons will tesselate with themselves. If you want to know why, calculate the angle measure for each of these shapes and you will see that each is a factor of 360. The same cannot be said for pentagons, heptagons, etc.
Can a regular heptagon tesselate?
No, it cannot.
Can you tesselate a regular octagon?
No, you cannot.
Can you tessellate five sided regular polygons by themselves?
five-sided polygons cannot tessellate
You cannot tessellate eight-sided regular polygons by themselves.?
True
You cannot tessellate eight-sided regular polygons by themselves?
true
You cannot tessellate six-sided regular polygons by themselves.?
False
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.
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.
Can a regular tessellation use four different regular polygons to cover a surface?
No. Four regular polygons cannot be combined for this purpose.
Is it true that you cannot tessellate seven sided polygons by themselves?
You cannot tessellate convex polygons with 7 or more sides.
You cannot tessellate eight-sided polygons by themselves?
True
