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How come not all regular polygons will tessellate? - Answers

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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How come not all regular polygons will tessellate? - Answers

https://math.answers.com/algebra/How_come_not_all_regular_polygons_will_tessellate

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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https://math.answers.com/algebra/How_come_not_all_regular_polygons_will_tessellate

How come not all regular polygons will tessellate? - Answers

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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      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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