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Tessellation


Date: 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/   
    
Associated Topics:
High School Geometry
High School Symmetry/Tessellations
High School Triangles and Other Polygons

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