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Why cant a regular pentagon be used to create a regular tessellation?
Wiki User
∙ 13y ago
it can tessellate
* * * * *
NO IT CANNOT!
A regular polygon can be used to create a regular tesselation if and only if its interior angle divides 360 degrees.
The interior angle of a regular pentagon is 108 degrees, which does not divide 360 degrees so it cannot be used for a regular tesselation.
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Three pentagons meeting at a point would cover 3*108 = 324 degrees - not enough to cover the 360 degrees at a point. Meanwhile 4 pentagons would cover 4*108 = 432 degrees - resulting in a 72 degree overlap.
Wiki User
∙ 13y ago
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why cant a regular tessellation use only pentagons?
A regular tessellation is one that uses regular polygons. An interior angle of a regular pentagon measures 108 degrees. A full circle, 360 degrees, is not divisible by 108 degrees. Consequently, it is not possible to arrange a number of polygons so that they meet at a point without gap or overlap.
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why cant a regular tessellation use only pentagons?
A regular tessellation is one that uses regular polygons. An interior angle of a regular pentagon measures 108 degrees. A full circle, 360 degrees, is not divisible by 108 degrees. Consequently, it is not possible to arrange a number of polygons so that they meet at a point without gap or overlap.
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