Message #540

From: Melinda Green <>
Subject: Re: [MC4D] higher dimensional book recommendations
Date: Mon, 21 Jul 2008 22:45:56 -0700

I haven’t read Jeffrey Weeks’ book though he did coauthor my favorite
Scientific American article of all time titled "Is Space Finite?"
which is related to the work I’ve done cataloguing infinite regular
polyhedra <>.
Of particular interest to members of our list might be his familiar
games you can play in such tiled spaces
<> which includes a nice
implementation of chess in toroidal space. I managed to beat it, but
only because it plays deterministically. If you try that, be sure to
switch from the "fundamental domain" mode to "tiling" mode. We exchanged
a few emails a long time ago and I found him to be a very nice and
approachable guy.

Professor Coxeter <> is most
definitely a giant of mathematics. His book Regular Polytopes
<> is quite possibly
the definitive work on the subject. It’s very dense reading but is a
great reference work to have around if only for the tables of 4D
vertices at the end. I consider it the bible of polyhedra. I was told
that he was a member of a polyhedra mailing list that I was on for
several years along with John Conway
<>, Mangus Wenninger
<> and others. He never
posted there but if he read the list then he probably read some of my posts.

I’m normally much more interested in scientist’s works than I am of the
people themselves but I love a good personal story too and will have to
read Coxeter’s. My favorite so far is The Man Who Loved Only Numbers:
The Story of Paul Erdos and the Search for Mathematical Truth
A really fun read about an amazing man.


Roice Nelson wrote:
> I’ve finished a couple books recently that I highly enjoyed and are
> apropos to the group.
> The Shape of Space
> <>
> by Jeffrey Weeks
> This does not require a deep math background - it is described as
> being at a high school level, but I really learned a ton and enjoyed
> it immensely. It is chock-full of dimensional analogy, interesting
> abstractions, and very fun to read with big, easy text and lots of
> pictures! It has also generated a number of thoughts for possible
> additional Rubik analogues in my mind. Briefly describing, the
> flexibility of topology opens up whole new worlds here, and if you
> abstract the original cube as just a 6-cell of faces on a topological
> sphere, all of a sudden there a veritable infinite number of new
> puzzles one could make. I’ve discussed possibly coding with my
> brother a 3D puzzle based on cell divisions of hexagons on a
> topological torus (e.g. a 12-cell is one option we did some sketches
> of; btw, the hexagonal tiling turns out to be important because 3
> cells still meet at each vertex). In the presentation we envision,
> the faces would have to stretch and deform when twisting due to the
> non-uniform curvature of a torus, but we hypercubists definitely don’t
> care about such appearances on our screen ;)
> King of Infinite Space: Donald Coxter, the Man Who Saved Geometry
> <>
> by Siobhan Roberts
> This is a biography of Donald Coxeter, a new intellectual hero of mine
> after reading it. I really love the genre of mathematical/scientific
> biographies, and this is a good one. The book is much more history
> than math, with plenty of enjoyable anecdotal stories about Coxeter
> and his peers (Hardy, Einstein, Von Neumann, etc.). Overall it is an
> engaging, sweet portrait of someone enthralled with polytopes for his
> entire life.