I've created six slide shows at Youtube featuring new classes of polyhedra,
including: Exploded, Lattice, Open and Crown polyhedra. You can find them by
typing in my name Albert P. Carpenter. I hope you find them interesting.
                                                    Thanx, Albert

Chemists Influence Stem-Cell Development With Geometry

http://www.sciencedaily.com/releases/2010/03/100317162000.htm

Just some food for thought. Wish there had been pictures of the patterns used.

Be certain to go into the gallery and look at the structures.  My little guy
(now 8) loves trying to build them out of zome (gumdrops and
toothpicks--whatever he can get his hands on quick enough :-)


--- In Polytopia@yahoogroups.com, jennifer kurtz <jenniyoungkurtz@...> wrote:
>
> Have you found this site? 
>  
> http://chemistry.ctrl.ucla.edu/crmr/
>
> Not exactly what you were wanting but worth looking at if you haven't yet.
>  
> Peace~ Jenn
> --- On Thu, 3/18/10, jxandar <jxandar@...> wrote:
>
>
>

"Teams had to use exactly 680 glasses to build a tower exactly 15 levels high with only one glass on top." Notice that it doesn't have to be a perfect pyramid!

--- In Polytopia@yahoogroups.com, "Johan E. Mebius" <jemebius@...> wrote:

> I am looking forward to a contest where several teams each handle 4900
> cannonballs instead of 55, some teams starting with a 70x70 square,
> the others starting with a square pyramid in 24 layers!

> (1x1 at the top, 2x2, 3x3 etc ending in 24x24 at the bottom)

> The game will be named "THE 4900".

> Cheers: Johan

> --- In Polytopia@yahoogroups.com, "Alan Michelson"
> amichelson2002@ wrote:

> > Then there was the recent Amazing Race episode where the players had to
> > catch a bus in Poland, and they had to go past the cuboctahedra. You can
> > see that on Photo Albums
> > <http://tech.ph.groups.yahoo.com/group/Polytopia/photos?m=> >
> > Miscellaneous
> > <http://tech.ph.groups.yahoo.com/group/Polytopia/photos/browse/7979> >
> > Amazing-Race-VE.

> > --- In Polytopia@yahoogroups.com, "Alan Michelson" <amichelson2002@>
> > wrote:

> > > Did you see last week's Amazing Race
> > <http://www.cbs.com/primetime/amazing_race6/show/ep06/index3.shtml> ?
> > > They had to stack (1^2) + (2^2) + (3^2) + (4^2) + (5^2) = 55
> > > cannonballs in a square-based pyramid!

Yes, it's all there at http://www.ac-noumea.nc/maths/polyhedr/CCP_.htm

--- In Polytopia@yahoogroups.com, "Michael Donovan" wrote:
>
> Back to the 12 around one associated with the cubeoctahedron..., I
> went to those sites, drawings.  We must be precise in math and that is
> why all the terms.  My head was spinning.  But do you see that the 12
> around one shape not 'cannon ball packed' would never fit in any
> packing pattern except that it be on one of the edges?  That is the
> main point I am trying to make.  Haviing trouble with the terms.
> Michael
>

--- In Polytopia@yahoogroups.com, "Alan M" <a.Michelson@...> wrote:
>
>
> --- In Polytopia@yahoogroups.com, "Alan Michelson" wrote:
> >
> > --- In Polytopia@yahoogroups.com, "Alan Michelson"
> > wrote:
> > >
> > > You are absolutely correct that it came from the Stella program.
> > > These four planes have Miller indexes of (±1,±1,±1). Now, what
> > > do you mean
> > > by the three primary? Do you mean (±1,0,0) & (0,±1,0) &
> > > (0,0,±1) ?
> > >
> > > Each color represents a set of planes that are perpendicular to
> > > a cube's body diagonal. The cube's body diagonals have Miller
> > > indexes of [±1,±1,±1].
> > >
> > > Primary colors can be red-yellow-blue or red-green-blue. Notice
> > > why the arbitrary colors red-yellow-green-blue were chosen: Just
> > > mosey down to your local neighborhood toy store and you will see
> > > that the toys are colored with plenty of reds & yellows & greens
> > > & blues. In fact, while you are in that toy shop, you will
> > > notice that the regular Polydron (ages 4+ years) are in these
> > > very same colors!

"These six elementary colors are frequently chosen to paint educational toys, or
for designs that try to appeal from their simplicity (such as the Olympic flag
and the Microsoft Windows logo)."

> > But JOVO <http://www.jovotoys.com/>  has 6 colors: red, yellow,
> > blue, green, black, white!
>
> Just look at the http://en.wikipedia.org/wiki/Natural_Color_System
>
>

Come visit my new Platonic Solids facebook page at:

http://www.facebook.com/pages/PlatonicSolids/158392277523641

--- In Polytopia@yahoogroups.com, Alan Michelson <amichelson2002@...> wrote:
>
>
> Tetraxis magnetic geometry puzzle
>
>
> This uses the same four colors based on the Natural Color System.
> Thanks to Jane of synergeo for this one! This one might be based on
> the oct-tet IVM. Notice the four colors on the pyramidal dents.

It might also be based on the rhombic dodecahedron. Those 4-color pyramidal
dents might be the dents of the rhombic dodecahedron rather than of the regular
octahedron. Notice the 3-valent dents, possibly of the rhombic dodecahedron.
I've also seen hints of the cuboctahedron, which is a part of the oct-tet IVM.
The 24-cell can have a cuboctahedron or a rhombic dodecahedron as its
projection. After all, the truncated rhombic dodecahedron and the truncated
octahedron do look similar.

> --- On Mon, 9/13/04, Michael Donovan <michael1@...> wrote:
> From: Michael Donovan <michael1@...>
> Subject: Re: [Polytopia] Having Some Code Fun in Tiling
> To: Polytopia@yahoogroups.com
> Date: Monday, September 13, 2004, 12:25 PM
>
>
>
>
>
>
> Wonderful image,
> But the primary colors fit in another way, those four planes are
> combinations of the three primary.  Looks like on of Robert Webbs
> animations from Stella

>   ----- Original Message -----
>   From: Alan Michelson
>   To: Polytopia@yahoogroups.com
>   Sent: Monday, September 13, 2004 2:57 PM
>   Subject: Re: [Polytopia] Having Some Code
>   Fun in Tiling

>   rybo6 <rybo6@...>
> wrote:
>
>     http://www.codefun.com/Geometry_tile1.htm
>
> Rybo

>   By the way, if you go to that web page, notice
>   the tetrahedron at
>   http://www.codefun.com/Images/Geometry/DodecTile/image004.jpg
>   Each vertice of the tetrahedron has a color that
>   matches its opposite face. This is because if you were to truncate
>   each vertice, you will get a plane that is parallel to and
>   therefore matches its opposite face. You can see this in
>   You could also see the red, yellow, green, blue color-coded planes
>   in http://www.superliminal.com/geometry/infinite/stereo/
>
> The upper picture has truncated tetrahedra.
> The lower picture has truncated octahedra.
>
> These were built using Polydron. The colored hexagons are oriented
>   according to the corresponding tetrahedron planes.
>
>
> You can see how this applies to the coloring problem in
>   http://www.codefun.com/Images/Geometry/DodecTile/image006.jpg
>

Hi Alan

On Sun, 17 Oct 2010, Alan M wrote:
>> Tetraxis magnetic geometry puzzle
>>
>> This uses the same four colors based on the Natural Color System.
>> Thanks to Jane of synergeo for this one! This one might be based on
>> the oct-tet IVM. Notice the four colors on the pyramidal dents.
>
> It might also be based on the rhombic dodecahedron. Those 4-color
> pyramidal dents might be the dents of the rhombic dodecahedron rather
> than of the regular octahedron. Notice the 3-valent dents, possibly of
> the rhombic dodecahedron. I've also seen hints of the cuboctahedron,
> which is a part of the oct-tet IVM. The 24-cell can have a cuboctahedron

There is a wooden version of the puzzle here

     http://www.johnrausch.com/PuzzleWorld/puz/augmented_second_stellation.htm

(And a similar icosahedral version

     http://www.johnrausch.com/PuzzleWorld/puz/jupiter.htm )

If you twist a tensegrity based on an octahedron there is
a point where the struts align in parallel sets of three
like the pieces of this puzzle

     http://www.antiprism.com/album/835_tens_models/tens_12_Lrg.jpg.0.html

Adrian
--
Adrian Rossiter
adrian@...
http://antiprism.com/adrian

It's based on the rhombic dodecahedron.  I will soon post on www.tetraxis.com a
link to a youtube video called "Tetraxis Geometry".  The rhombic dodecahedron is
a space filler.  Also, the rhombic dodecaherdron together with a triangular
prism fill space.

John Kostick was building these types of configurations of sticks (not as
puzzles) out of both round and triangular-shaped rods back in the mid 1960's,
prior to Stewart Coffin's wooden puzzles came out in the 70's, but yes, the
outside shape of the object is the same.

Here's another link to wooden versions:
http://www.jjkostick.com/Jane_Kostick/tetraxis.html

The link to a page that shows some of John's earlier work can be seen here:
http://www.jjkostick.com/John_Kostick/Stars.html

-Jane

--- In Polytopia@yahoogroups.com, Adrian Rossiter <adrian_r@...> wrote:
>
> Hi Alan
>
> On Sun, 17 Oct 2010, Alan M wrote:
> >> Tetraxis magnetic geometry puzzle
> >>
> >> This uses the same four colors based on the Natural Color System.
> >> Thanks to Jane of synergeo for this one! This one might be based on
> >> the oct-tet IVM. Notice the four colors on the pyramidal dents.
> >
> > It might also be based on the rhombic dodecahedron. Those 4-color
> > pyramidal dents might be the dents of the rhombic dodecahedron rather
> > than of the regular octahedron. Notice the 3-valent dents, possibly of
> > the rhombic dodecahedron. I've also seen hints of the cuboctahedron,
> > which is a part of the oct-tet IVM. The 24-cell can have a cuboctahedron
>
> There is a wooden version of the puzzle here
>
>     http://www.johnrausch.com/PuzzleWorld/puz/augmented_second_stellation.htm
>
> (And a similar icosahedral version
>
>     http://www.johnrausch.com/PuzzleWorld/puz/jupiter.htm )
>
> If you twist a tensegrity based on an octahedron there is
> a point where the struts align in parallel sets of three
> like the pieces of this puzzle
>
>     http://www.antiprism.com/album/835_tens_models/tens_12_Lrg.jpg.0.html
>
> Adrian
> --
> Adrian Rossiter
> adrian@...
> http://antiprism.com/adrian
>

Hi Jane

On Wed, 20 Oct 2010, Jane wrote:
> It's based on the rhombic dodecahedron.  I will soon post on
> www.tetraxis.com a link to a youtube video called "Tetraxis Geometry".
> The rhombic dodecahedron is a space filler.  Also, the rhombic
> dodecaherdron together with a triangular prism fill space.
>
> John Kostick was building these types of configurations of sticks (not
> as puzzles) out of both round and triangular-shaped rods back in the mid
> 1960's, prior to Stewart Coffin's wooden puzzles came out in the 70's,
> but yes, the outside shape of the object is the same.
>
> Here's another link to wooden versions:
> http://www.jjkostick.com/Jane_Kostick/tetraxis.html

Nice models and puzzles.

There are also some models and discussion of the arrangement
in Alan Holden's Shapes, Space and Symmetry from 1971 (pages
160-162 in the Dover edition). The dead link on my tensegrity
page pointed to a page that included photos from the book.
Here is a copy of the page on the wayback machine

    
http://web.archive.org/web/20050217120032/http://memeticdrift.net/tau/4axesb.htm

Adrian.
--
Adrian Rossiter
adrian@...
http://antiprism.com/adrian

--- In Polytopia@yahoogroups.com, Adrian Rossiter <adrian_r@...> wrote:

> Hi Alan

> On Sun, 17 Oct 2010, Alan M wrote:

> >> Tetraxis magnetic geometry puzzle

> >> This uses the same four colors based on the Natural Color System.
> >> Thanks to Jane of synergeo for this one! This one might be based on
> >> the oct-tet IVM. Notice the four colors on the pyramidal dents.

> > It might also be based on the rhombic dodecahedron. Those 4-color
> > pyramidal dents might be the dents of the rhombic dodecahedron rather
> > than of the regular octahedron. Notice the 3-valent dents, possibly of
> > the rhombic dodecahedron. I've also seen hints of the cuboctahedron,
> > which is a part of the oct-tet IVM. The 24-cell can have a cuboctahedron

> There is a wooden version of the puzzle here
> http://www.johnrausch.com/PuzzleWorld/puz/augmented_second_stellation.htm

> (And a similar icosahedral version
> http://www.johnrausch.com/PuzzleWorld/puz/jupiter.htm )

> If you twist a tensegrity based on an octahedron there is
> a point where the struts align in parallel sets of three
> like the pieces of this puzzle
> http://www.antiprism.com/album/835_tens_models/tens_12_Lrg.jpg.0.html

This could happen with chiral (T, O, I) symmetry. The polygon faces are twisted from being involute (that is, the opposite faces are inverted with respect to each other due to the diameters going through a central point) to being aligned (that is, the polygons can become the ends of a prism!) You can see an example where the pentagons are aligned.

Notice that the opposite faces of a jitterbug are always involute to each other. This is because the jitterbug doesn't have chiral symmetry, but rather pyritohedral symmetry. (Think of the alternating faces of an octahedron rotating in opposite directions; the faces are rotating together on the same axis and can never twist!)

> Adrian
> --
> Adrian Rossiter
> adrian@...
> http://antiprism.com/adrian

The video illustrating the geometry of the Tetraxis is now up on
YouTube...here's the link:
http://www.youtube.com/watch?v=WnkyOTtBij8

The video was created by Ken Fan and produced by Girls' Angle, a math club for
girls in Cambridge, MA. www.girlsangle.org
The video was made using Blender, a powerful, free, open source 3D creation
suite (www.blender.org).

-Jane

Hi Jane

On Thu, 21 Oct 2010, Jane wrote:
> The video illustrating the geometry of the Tetraxis is now up on
> YouTube...here's the link: http://www.youtube.com/watch?v=WnkyOTtBij8

I like the video, it explains how everything fits together
very well.

There is a point in the video where the rhombic dodecahedra
are shown in isolation. I made an animation earlier in the
year showing how this vertex-joined arrangement could close
down to fill space. That is, if you remove the triangular rods
but keep the rhombic dodecahedra and their connections then
the free space can be closed down this way

    
http://www.antiprism.com/album/805_plane_space_jbugs/squ_jit_rd_Med.jpg.9.html

Adrian.
--
Adrian Rossiter
adrian@...
http://antiprism.com/adrian

You're just treating each rhombic dodecahedron as if it were a jitterbugging
square:
http://www.antiprism.com/album/805_plane_space_jbugs/squ_jit_Med.jpg.7.html

--- In Polytopia@yahoogroups.com, Adrian Rossiter <Adrian_r@...> wrote:
>
> Hi Jane
>
> On Thu, 21 Oct 2010, Jane wrote:
> > The video illustrating the geometry of the Tetraxis is now up on
> > YouTube...here's the link:
> http://www.youtube.com/watch?v=WnkyOTtBij8
>
> I like the video, it explains how everything fits together
> very well.
>
> There is a point in the video where the rhombic dodecahedra
> are shown in isolation. I made an animation earlier in the
> year showing how this vertex-joined arrangement could close
> down to fill space. That is, if you remove the triangular rods
> but keep the rhombic dodecahedra and their connections then
> the free space can be closed down this way
>
>http://www.antiprism.com/album/805_plane_space_jbugs/squ_jit_rd_Med.jpg.9.html
>
> Adrian.
> --
> Adrian Rossiter
> Adrian@...
> http://antiprism.com/adrian
>

--- In Polytopia@yahoogroups.com, "Jane" <jjkostick@...> wrote:

> The video illustrating the geometry of the Tetraxis is now up on YouTube...here's the link:
> http://www.youtube.com/watch?v=WnkyOTtBij8

Take a rhombic dodecahedron. Add more rhombic dodecahedra on the 4-fold vertices so that they are along the Cartesian XYZ axis. Add more rhombic dodecahedra on the 3-fold vertices so that they are along the Quadray axis. Notice that the color scheme is similar to the Coxeter-Dynkin 3-space groups of Wikipedia. Now look along the 3-fold views until you see something that resembles the Magen David. You now see equilateral-triangle spaces where the rods can come through.

> The video was created by Ken Fan and produced by Girls' Angle, a math club for girls in Cambridge, MA. www.girlsangle.org
> The video was made using Blender, a powerful, free, open source 3D creation suite (www.blender.org).

> -Jane

http://groups.yahoo.com/group/synergeo/messages/63530?threaded=1&m=e&tidx=1

--- In Polytopia@yahoogroups.com, Alan Michelson <amichelson2002@...> wrote:
>
> By the way, if you notice the tetrahedral packing , then you will notice that
it is quite similar to the cuboctahedral packing . They both have the same ABC
layering as in http://physics2000.web1000.com/abaabc.html
> Just get your Chroma-Depth glasses and you can see what I mean in 3-D! Notice
that if you take off the corner balls off of the tetrahedral pack that you are
left with an octahedral sphere packing. This is similar to a ball at each vertex
of the IVM, which the cuboctahedron is a subset of.
>
> Michael Donovan <michael1@...> wrote:
> No, and this is an important point.  This is why Kepler and others did not
follow this path. He was so close to it.  Just not for his time or whatever. 
Thinking of his letter either Midnight Reflections On The Six Cornered Snowflake
or was it New Years Reflection On The Six Cornered Snowflake.
>     The packing you point to is a tetrahedron and is part of a tetrahedral
progression.  If this is built out you could take out any group and have a
'close pack' of balls pilled the way cannon balls would pile.  If you take six
balls and fit them around one on a surface, say you glue them.  Take two
separate groups of three glued together.  Now place one group of three on the
top it will fit into one alternating group of three of the six pockets around
the central ball.  Say you glue that.  You have the last group of three to glue
on the other side, the other side of six around one in a plane.  Now, if you
glue the next group of three in the same pockets, you will have made a structure
that will fit nicely anywhere inside the 'cannonball' packing (or inside that
tetra someplace if the tetra was extended with many balls).  This is NOT the
core central shape that reflects as the 3-D zodiac, producer of cabala map,
crystal symmetry conditions, di da di da.  But if you twist the group
>  of three so that it sits in the alternating pockets it IS.  And then, using
your imagination, any which way you turn this and look at any triangle the
triangle on the other side will be pointing the other way making the Star of
David.  Now this shape can only sit on an edge of that packing.  And if you pack
around it you will need to change the direction of the pack, balls fitting in
another set of holes.  And this core shape, the solar crystal, must be on one of
four interfaces in this manner.  And those interfaces are the four planes which
if any moved, produce a tetrahedron.
> You might ask why is a 'central' shape always on an interface.  So it can
remain central.  If not it would be 'locked in'.  The assumption is that
everything is in motion, in vibration and twists.  This is why 'sphere-packers'
ignored the central shape.  It 'seemed' irregular.
> Michael Donovan
>
>
>
> ---------------------------------

Hello,

I have made a few short clips on the nature of three spheres interacting which
you may find of use (for illustrative purposes) or interesting.

http://www.youtube.com/watch?v=MCrf8aN7YMY
http://www.youtube.com/watch?v=fySkSjG_DU4
http://www.youtube.com/watch?v=soRj7SyY818
http://www.youtube.com/watch?v=Mcq9fP4N9ag
http://www.youtube.com/watch?v=nDH9JL2Aduw
http://www.youtube.com/watch?v=wcX_yKkEyUA

Best,

James

greetings fellow Polytopians
I cant seem to find it or remember what it was called, but someone here posted a
table of all the polyhedron formulas such as the circumferences radii, and the
strut length.
Can any one locate that for me please, I still want to CSG model them in
TurboCAD...

--- In Polytopia@yahoogroups.com, "cdsgraphics1952" <cdsgraphics@...> wrote:
>
> greetings fellow Polytopians
> I cant seem to find it or remember what it was called, but someone here posted
a table of all the polyhedron formulas such as the circumferences radii, and the
strut length.
> Can any one locate that for me please, I still want to CSG model them in
TurboCAD...

Hi all:

Some pertinent info for the Platonic and Archimedean Solids here:

	 http://www.geometrycode.com/sg/polyhedra.shtml
(with links to all the fold-up patterns for the 5 + 13), and loads of links
here:

	 http://www.geometrycode.com/resources.shtml

Cheers! :-)

---------
The Geometry Code screensaver + more:
	 http://www.GeometryCode.com
Sacred Geometry Design Sourcebook:
	 http://www.Lulu.com/content/583170
Free monthly email bulletin on sacred geometry and related subjects:
	 http://www.GeometryCode.com/subscribe.shtml
Geometric logos, graphics, CMS-based web design, media, fine art, photography:
	 http://www.IntentDesignStudio.com
Bruce Rawles  POB 431, Ashland, Oregon 97520; skype: BruceRawles
	 http://www.BruceRawles.com
Free monthly email bulletin on A Course In Miracles - events, media and
resources:
         http://www.ACIMblog.com/subscribe
Our world travel gallery and more:
	 http://www.FlyingCatTravel.com
http://twitter.com/BRGeometryCode
http://www.facebook.com/Bruce.Rawles
http://www.linkedin.com/in/BruceRawles
---------

thanks for that resource.
I've Bookmarked it for examination later.
The one previously posted (here?)had the actual formula expressions that
caluulate the answers that is in this one you show
I may have by by amichelson2002, though I cant find it here/
Thanks
Craig

--- In Polytopia@yahoogroups.com, "BruceRawles" <bruce@...> wrote:
>
> --- In Polytopia@yahoogroups.com, "cdsgraphics1952" <cdsgraphics@> wrote:
> >
> > greetings fellow Polytopians
> > I cant seem to find it or remember what it was called, but someone here
posted a table of all the polyhedron formulas such as the circumferences radii,
and the strut length.
> > Can any one locate that for me please, I still want to CSG model them in
TurboCAD...
>
> Hi all:
>
> Some pertinent info for the Platonic and Archimedean Solids here:
>
>  http://www.geometrycode.com/sg/polyhedra.shtml
> (with links to all the fold-up patterns for the 5 + 13), and loads of links
here:
>
>  http://www.geometrycode.com/resources.shtml
>
> Cheers! :-)
>
> ---------
> The Geometry Code screensaver + more:
>  http://www.GeometryCode.com
> Sacred Geometry Design Sourcebook:
>  http://www.Lulu.com/content/583170
> Free monthly email bulletin on sacred geometry and related subjects:
>  http://www.GeometryCode.com/subscribe.shtml
> Geometric logos, graphics, CMS-based web design, media, fine art, photography:
>  http://www.IntentDesignStudio.com
> Bruce Rawles  POB 431, Ashland, Oregon 97520; skype: BruceRawles
>  http://www.BruceRawles.com
> Free monthly email bulletin on A Course In Miracles - events, media and
resources:
>         http://www.ACIMblog.com/subscribe
> Our world travel gallery and more:
>  http://www.FlyingCatTravel.com
> http://twitter.com/BRGeometryCode
> http://www.facebook.com/Bruce.Rawles
> http://www.linkedin.com/in/BruceRawles
> ---------
>

actually I found it here just now in
Files > Polyhedra_Dimensions as separate files...
I thought I was looking for a Table that had all of them in one
But this will do nicely...

--- In Polytopia@yahoogroups.com, "cdsgraphics1952" <cdsgraphics@...> wrote:
>
> thanks for that resource.
> I've Bookmarked it for examination later.
> The one previously posted (here?)had the actual formula expressions that
caluulate the answers that is in this one you show
> I may have by by amichelson2002, though I cant find it here/
> Thanks
> Craig
>
> --- In Polytopia@yahoogroups.com, "BruceRawles" <bruce@> wrote:
> >
> > --- In Polytopia@yahoogroups.com, "cdsgraphics1952" <cdsgraphics@> wrote:
> > >
> > > greetings fellow Polytopians
> > > I cant seem to find it or remember what it was called, but someone here
posted a table of all the polyhedron formulas such as the circumferences radii,
and the strut length.
> > > Can any one locate that for me please, I still want to CSG model them in
TurboCAD...
> >
> > Hi all:
> >
> > Some pertinent info for the Platonic and Archimedean Solids here:
> >
> >  http://www.geometrycode.com/sg/polyhedra.shtml
> > (with links to all the fold-up patterns for the 5 + 13), and loads of links
here:
> >
> >  http://www.geometrycode.com/resources.shtml
> >
> > Cheers! :-)
> >
> > ---------
> > The Geometry Code screensaver + more:
> >  http://www.GeometryCode.com
> > Sacred Geometry Design Sourcebook:
> >  http://www.Lulu.com/content/583170
> > Free monthly email bulletin on sacred geometry and related subjects:
> >  http://www.GeometryCode.com/subscribe.shtml
> > Geometric logos, graphics, CMS-based web design, media, fine art,
photography:
> >  http://www.IntentDesignStudio.com
> > Bruce Rawles  POB 431, Ashland, Oregon 97520; skype: BruceRawles
> >  http://www.BruceRawles.com
> > Free monthly email bulletin on A Course In Miracles - events, media and
resources:
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Polytopia Group Participants,

A new book has just been released by Foundation Encyclopedia Dialectica
[F.E.D.], entitled --

A Dialectical "Theory of Everything" -- Meta-Genealogies of the Universe and of
Its Sub-Universes: A Graphical Manifesto.

-- see:

http://www.adventures-in-dialectics.org/Adventures-In-Dialectics/Adventures-In-D\
ialectics-entry.htm


Texts preparatory to this book are available for free download via --

http://www.dialectics.org/dialectics/Primer.html


I could be wrong on this one, of course, but I think it may accomplish, for
Platonian and Hegelian Dialectic, +, at long last, what Boole did for
Aristotelian syllogistic, +, formal logic with his 1847 "The Mathematical
Analysis of Logic", and with his 1854 "Investigation of the Laws of Thought"!


Here's the text from the front and back "flaps" of the "dust cover" jacket
[modified for this list's typography] --

"A Dialectical Theory of Everything — Meta-Genealogies of the Universe and of
Its Sub-Universes: A Graphical Manifesto.


Volume 0:  Foundations [Edition 0 – Dec. 2010, from F.E.D. Press]

This initial volume, Volume 0, sets forth the foundations of F.E.D.'s
dialectical-mathematical "model of everything".

Synthesizing ancient themes of dialectic, "autokinesis", and 'self-refluxivity'
['karmicity'], with modern themes of logical and set-theoretical paradox as
"self-reflexivity", and of integro-differential equation "nonlinearity", evoked
via both occidental and oriental sources from antiquity, and via modern
developments in natural/social science, and in mathematics, this initial volume
lays out foundations for a unified theory of dialectic.

Foundations presented include a unified theory of the traditions of Platonian
and Hegelian dialectic, and the discovery, for the first time in human history,
of a rich and versatile 'mathematics of dialectic'.

This new 'mathematics of dialectic' is utilized to derive a seventeen-symbol
equation, which models, qualitatively [via ontological categories], the
dialectical self-evolutions, and 'self-meta-evolutions', of our "kosmos" as a
totality, which  also predicts a next major self-development of this "kosmos",
and which summarizes the dialectical "theory of everything" that gives this work
its title.

A dialectical, 'ideo-ontological' categorial progression of systems of generally
'qualo-quantitative', dialectical arithmetics, are modeled, using the second
system  in that progression, its first explicitly dialectical system, starting
from "Natural Numbers", or N, arithmetic, as purely-quantitative [implicitly,
'pre-vestigially <<aufheben>>-dialectical via its Peano successor-function]
first system.

The second system is a 'purely-qualitative' [purely ontological],
"non-standard model" of "standard" N arithmetic [i.e., the first four, "first
order"  Peano Postulates hold for this system as well as for the N system], 
with a 'contra-Boolean' algebra, founded upon a hitherto-unnoticed, strong
negation of Boole's "Fundamental Law of [formal-logical] Thought".


Volume 1:  Geneses [forthcoming, from F.E.D. Press]

Volume 1 recounts the genesis of the new dialectical mathematics in detail.


Volume 2:  Dialectical 'Meta-Models' of the 'Human Phenome' [forthcoming, from
F.E.D. Press]

Volume 2 presents 'psycho-historical dialectical meta-models' , expressed via
the new dialectical mathematics, which zoom-in on human-social constructions,
including a 'meta-model' of the genesis of written language, a 'meta-model' of
the development of ancient Mediterranean philosophy, and a 'meta-model' of the
development of the "standard" arithmetics, starting from the N arithmetic as
"arche'".


Volume 3:  The Dialectic of Nature [forthcoming, from F.E.D. Press]

Volume 3 explores 'self-meta-evolutions' of human society, modeled via the new
dialectical mathematics, as processes of later natural history, including those
of the human-social relations, and of the human-social forces, of human-societal
self-reproduction.

It also addresses the parallel development of related human thought-modes,
including an historical-dialectical mathematical  'meta-model' of the 'dialectic
of the dialectic itself', as well as detailing the development of the "Theory of
Everything", "Dialectic of Nature Equation" 'meta-model' of the <<kosmos>> as a
whole."

Regards,

Miguel