does a regular 22-gon tessellate the plane? does a regular 40-gon tessellate the plane?
1
Expert's answer
2013-05-02T10:13:32-0400
A tessellation is createdwhen a shape is repeated over and over again covering a plane without any gaps or overlaps. Since 180(x-2) equals how many degrees it has, 180(22-2)= 180(20)= 180 x 20= 3600 To find only ONE angle you need to divide 3600 by 22, yielding 163.6. 360 divided by 163.6 is 2.2 , not an integral number. This shows that a 22-gon doesn't tessellate. and 180(40-2)= 180(38)= 180 x 38= 6840 To find only ONE angle you need to divide 6840 by 40, yielding 171. 360 divided by 171 is 2.1 , not an integral number. This shows that a 40-gon doesn't tessellate.
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Assignment Expert
21.05.19, 10:57
A regular dodecagon (12-gon) will not tesselate because one interior
angle of this polygon is 180*(12-2)/12=150 degrees, but 360 is not
divisible by 150 (indeed, 360/150=2.4).
Courtney Montero
21.05.19, 05:06
could a regular dodecagon be used as a basic unit for a tessellation?
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Comments
A regular dodecagon (12-gon) will not tesselate because one interior angle of this polygon is 180*(12-2)/12=150 degrees, but 360 is not divisible by 150 (indeed, 360/150=2.4).
could a regular dodecagon be used as a basic unit for a tessellation?
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