What is a tessellation?

Date: 01/20/97 at 18:33:40
From: andrew
Subject: Geometry (tessellation)

What is a tessellation?  Can you give an example?

Thank you.

Date: 01/21/97 at 22:45:34
From: Doctor Wallace
Subject: Re: Geometry (tessellation)

Hi Andrew!

A regular tessellation is a covering of a plane by identical shapes.

Imagine that you have a room in your house that you'd like to outfit 
with a new floor. You want to completely cover the floor with tile, so 
that it looks nice. You don't want any gaps or holes showing between 
the tiles. Also, you can only have one shape of tile. You can use as 
many tiles as you need, so that the whole floor is covered, but every 
tile has to be perfectly identical to every other tile.  

If you can completely cover the floor with a certain shape of tile, we 
say that that shape "tessellates" the floor. With some shapes, you'll 
be able to cover the floor, and with others, you won't. If you try 
using a hexagon, for example, you'll succeed. This is because each 
hexagon snuggles nicely beside the others, with no gaps in between.  
But if you try to use an octagon, you'll fail.  Octagons do not 
snuggle nicely.  Try cutting some octagons and hexagons out of paper 
and you'll see what I mean.

For lots more information, see Suzanne Alejandre's "Tessellation 
Tutorials" at 

  http://mathforum.org/sum95/suzanne/tess.intro.html   

Thanks for writing, Andrew!

-Doctor Wallace,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/