Norman Johnson's Uniform Polytopes manuscript (2000)

Discussion of tapertopes, uniform polytopes, and other shapes with flat hypercells.

Norman Johnson's Uniform Polytopes manuscript (2000)

Postby ytrepus » Thu Feb 06, 2014 11:54 pm

Hello,

I see a lot of reference to a manuscript or unpublished work by Norman Johnson on Uniform Polytopes -- apparently it was going to be published in 2000 but I cannot locate any information on it anywhere. Sometimes it is referred to as his "forthcoming book".

Does anyone know what has happened to this, and is there anywhere to purchase it?

Thanks a lot,
Rob
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Re: Norman Johnson's Uniform Polytopes manuscript (2000)

Postby quickfur » Fri Feb 07, 2014 1:14 am

I wanna know too!! Is it published yet or still just a manuscript??
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Re: Norman Johnson's Uniform Polytopes manuscript (2000)

Postby wendy » Fri Feb 07, 2014 7:41 am

I'm supposed to get a mention in there for the laminatruncate x4x3o8o, and the tiling of o3x4x3o, 64 to a corner.
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the dream we dream together is reality.

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Re: Norman Johnson's Uniform Polytopes manuscript (2000)

Postby Klitzing » Fri Feb 07, 2014 1:24 pm

quickfur wrote:I wanna know too!! Is it published yet or still just a manuscript??


Well, I do not know either. - Here what I can recover about its status:

On 1996 / 9 / 7 Norman Johnson wrote within a private mailing list as an announcement of his forthcoming book:
Norman Johnson wrote:...

My forthcoming book, Uniform Polytopes, to be published in 1997 by
Cambridge University Press, deals with regular and uniform figures in both
Euclidean and non-Euclidean space of arbitrary dimension. By "figures" I
mean polytopes (e.g., polyhedra), honeycombs (e.g., tessellations), and
compounds like the pairs of simplexes whose properties George Olshevsky
has been exploring. There is even some discussion of regular complex
polytopes and of regular skew polygons and polyhedra, partly because these
are interesting generalizations of regular figures in the usual sense and
partly because many regular complex or skew figures are closely related to
uniform "real" figures. I try to be a little more even-handed than many
writers (even Coxeter) in describing the possible realization of regular
and uniform figures in hyperbolic or elliptic space as well as their more
familiar Euclidean forms.

Still, the heart of the book is the description and depiction of the
uniform polyhedra, consisting of the Platonic and Archimedean solids, the
uniform prisms and antiprisms, the Kepler-Poinsot polyhedra, and the other
uniform star polyhedra discovered in last half of the nineteenth century
and the first half of the twentieth. The standard reference here is, of
course, the 1954 paper of Coxeter, Longuet-Higgins, and Miller, with the
best nontechnical exposition being the 1971 book of Magnus Wenninger. My
book will have original line drawings by Arthur Norman of the University
of Cambridge Computer Laboratory. In addition, there will be a treatment
of the uniform compound polyhedra enumerated by John Skilling in 1976,
with computer-generated drawings of many of them.

...

Norman W. Johnson
Department of Mathematics
Wheaton College
Norton, Massachusetts 02766


On 1999 / 1 / 13 Norman Johnson then wrote there towards its status:
Norman Johnson wrote: ####### has inquired about the status of my forthcoming book
Uniform Polytopes. The book will contain nine chapters:

1. Polytopes and Honeycombs
2. Geometries and Transformations
3. Symmetry Groups
4. Uniform Polyhedra and Tessellations
5. Uniform Figures of Higher Rank
6. Uniform Star Polychora
7. Regular Figures
8. Plane and Solid Compounds
9. Higher-dimensional Compounds

It will have numerous line drawings produced by Arthur C. Norman of the
University of Cambridge Computer Laboratory, nine supplementary tables,
and an extensive bibliography.

The only part not yet finished is Chapter 6, which will include both
a discussion of the underlying theory and a description of some of the
figures recently discovered by Jonathan Bowers and George Olshevsky. I
expect to have the manuscript completed and sent to the editors at
Cambridge University Press by April or May. If all goes well, it should
appear sometime next year.

Norman


On 2005 / 8 / 19 Norman then wrote to the same list:
Norman Johnson wrote:...

######### and others have inquired about the status of my book on
uniform polytopes, which is to be published by Cambridge University Press
as part of its Encyclopedia of Mathematics. I have essentially completed
the manuscript, which comprises nine chapters, eight tables, and a copious
bibliography. I have nearly finished preparing layouts for the many line
drawings that will accompany the text, though a number of the drawings have
yet to be created. I expect to be sending it all off to my editor fairly
soon, after which I may have a better idea of when it will finally be in
print. I will keep List subscribers informed of further developments.


Norman


And then on 2006 / 7 / 28:
Norman Johnson wrote:...
In a separate message, ####### asked about #######'s reference to an
early version of my Uniform Polytopes manuscript. It is not available
in electronic form, but it may not be too much longer before the book
is actually published.

Norman


Though, at least at the official website of Cambridge University Press, I still cannot spott that item.

--- rk
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Re: Norman Johnson's Uniform Polytopes manuscript (2000)

Postby ytrepus » Fri Feb 07, 2014 5:36 pm

Thanks a lot! That was very helpful. I do hope this gets published some day -- sounds like it would be a great read. I'm currently reading Coxeter's Regular and Uniform Polytopes I - III and learnign quite a bit from them.
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