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(A)/Periodic convex tilings (or near-tilings) of the plane or (3 space)

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  • Subject: [mg20907] (A)/Periodic convex tilings (or near-tilings) of the plane or (3 space)
  • From: "Kai G. Gauer" <gauer at>
  • Date: Sun, 21 Nov 1999 15:12:50 -0500 (EST)
  • References: <7v3bvj$> <7v6700$> <7vdq5i$>
  • Sender: owner-wri-mathgroup at

I am researching the topic of either periodic or non-periodic (usually) convex
tilings using congruent pieces of one or two or three shape pieces (or more, but,
usually where pieces should be allowed to be used infinitely often, only
sometimes necessary, or when a requirement of an additional piece set will be
necessary)  to do so in hopes to cover most and/or all of a plane (or a three
space) that extends infinitely out in all directions. A lot of the introductory
level material was apparently first brought to widespread attention in the latter
portion of the 20 th century in the math columns of Scientific American magazine.
I am currently studying Applied Abstract Algebra (Math 424 at U of Regina and had
come across the topic of tilings in a 1998 Springer book with the title as above
by Lidl & Pilz) and I am need of a research topic that relates to symmetry
groups. Unfortunately, my knowledge in the vastness of symmetry groups is weak
(I'd hope to improve my knowledge of them later by taking the intro level Modern
Algebra class later, but, I had to take the class now, since it wouldn't be
offered again in the near future) and I would hope to not be referred to post PhD
level papers in which I may or may not be able to fully understand. What I am
looking for however, is any source codes for Mathematica or for C (or another
MODERN, popular programming language which has good graphics output capabilities)
that enable a user to easily give plot sketchings and investigations to basic
grouping structures that tend to give some sort of nice tiling property that is
investigatable using a computer. I know of the basic 17 tilings of the plane, but
I would like to come up with a slightly more nontrivial example that I could use
as an example in a presentation. I would also prefer source code as opposed to a
picture of somebody's fancy wallpaper pulled off their homepage. Mathematica
packages that allow for undergarduate level experimentation would actually be
just fine, but I would consider looking at almost anything relating to the topic.

Thanks everyone for the help.

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