TessellationDate: 02/26/98 at 01:16:13 From: Stacey Subject: geometry Are there any non-regular convex polygons with more than four sides that can tessellate? Date: 02/26/98 at 09:27:25 From: Doctor Rob Subject: Re: geometry Absolutely! How about a pentagon that looks like a square with a triangle attached to one side? These can be lined up in strips with all the sides opposite the triangle lined up to make an infinite straight line. Two strips with the triangles pointing in diametrically opposite directions will fit together to make a larger strip with two straight edges, which can obviously tesselate the plane. The triangle doesn't have to be isosceles, but can be general, as long as one side is as long as the side of the square, and the right or obtuse angle, if any, is opposite the attached side (to make the polygon convex). Diagram: ---------------------------------------------------------- | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | \ _.-'\ _.-'\ _.-'\ _.-'\ _.-'\ \ _.-' \ _.-' \ _.-' \ _.-' \ _.-' \ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ---------------------------------------------------------- There are undoubtedly many others. Take the tessellation by regular hexagons and squeeze it along a direction perpendicular to one of the edges, so they are all tall and narrow. That would work, too. -Doctor Rob, The Math Forum Check out our web site http://mathforum.org/dr.math/ |
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