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Re: Scientists Say Universe May Be Soccer-Ball Shaped

🔗Bill Arnold <billarnoldfla@yahoo.com>

10/11/2003 10:24:47 PM

John Chalmers writes,

/celestial-tuning/message/131

"Tegmark also disagrees: The significance of the largest scale
CMB fluctuations in WMAP Ang�elica de Oliveira-Costa1, Max
Tegmark1, Matias Zaldarriaga2 & Andrew Hamilton3...We
investigate anomalies reported in the Cosmic Microwave
Background maps from the Wilkinson Microwave Anisotropy Probe
(WMAP) satellite on very large angular scales and discuss possible
interpretations. Three independent anomalies involve the quadrupole
and octopole: 1) The cosmic quadrupole on its own is anomalous at
the 1-in-20 level by being low (the cut-sky quadrupole measured
by the WMAP team is more strikingly low, apparently due to a
coincidence in the orientation of our Galaxy of no cosmological
significance... The simplest small universe model where the
universe has toroidal topology with one small dimension of order
half the horizon scale, in the direction towards Virgo, could
explain the three items above. However, we rule this model out
using two topological tests: the S-statistic and the matched circle
test. In particular, our results rule out the recently
proposed dodecahedron model of Luminet, Weeks, Riazuelo, Lehoucq
& Uzan"

Well, that's all, folks! The G-O-B-B-L-E-D-E-G-O-O-K of
pseudo-modern stellar astronomy has just gobbledegooked
in front of national T-U-R-K-E-Y day! Who are they trying
to K-I-D?

Why don't T-H-E-Y deal with some simple math of our solar-
planetary system, which *IS* as dodecahedrally spherical
as it gets:

In my papers
BODE'S LAW EXPLAINED and ON THE SPECIAL THEORY OF ORDER,
note the column 0,3,6,9,12,24,45,90,180,270,360, and note
that Kepler's shelled dodecahedrons fit the new predicted
analysis by modern astronomy, and thus the universe squares
the circle!

MUSIC OF THE SPHERES IS NEXT, as in "Play It Again, Monz!"

Hi, Spacepeople.

Looks interesting, and some of you might be interested
in my work, particularly on BODE'S LAW EXPLAINED and
ON THE SPECIAL THEORY OF ORDER. By way of introduction,
here are two posts, and some URLs, and I am willing to
respond to any and all questions.

Message 67 to Celestial-Tuning@yahoogroups.com
From: Bill Arnold <billarnoldfla@y...>
Date: Tue Oct 1, 2002 11:57 pm
Subject: Sunspot cycles, Weather and planetary synodic cycles

As a contributing science writer to the Foundation for the Study
of Cycles in the 1970s I wrote a number of articles on order in our
solar-planetary system, mainly on perceived correlation of the
sunspot cycle, weather and planetary synodic cycles round the sun.

An axiom of physics that should not be overlooked in any application
of mathematics to things in reality is that the general laws apply
universally. (See my previous papers in the Bulletin: "Bode's Law
Explained," Cycles 30: 82, 1979, and "On the Special Theory of
Order," Cycles 36: 219, 1985.) Therefore, if the clock pattern is
applied to our solar-planetary system--both systems involve objects
in 360-degree motion around their respective centers--any two planets
will cross only a certain number of times. Thereafter, the pattern
repeats. (see my paper: "Why the sunspot cycle 22 years long?"
Cycles 46: 3, 1996.)

As I pointed out in my previously cited papers, the primary cause of
the full-wave 22-year sunspot cycle is the Saturn-Uranus synodic
cycle. These two planets cross "only 22 times" before the pattern
repeats.

Whereas a clock has only two hands, the solar-planetary system is not
made up of a mere two planets; the cumulative effect of each set of
two planets must be computed as they relate to the others. In
addition, the solar-planetary electrical and magnetic field in which
the multitude of planets move and cross, is, itself, in motion with
respect to the center of the galaxy. Also, the planets are
precessing with respect to the distant star field. Consequently, our
solar-planetary system will not behave as methematically precise as a
clock. Indeed, each individual 22-year cycle varies immensely, from
about 20.8 to about 27 years.

In The Old Farmer's Almanac 1981, Guy Murchie popularized my theory
by reference to my publications, asking: "Is there order among the
planets? Or, as Pythagoras once put it, is there Music in the
Spheres?"

I published Arnold's Law in 1979, as follows:

Bodies_Proportion___Degreed Arcs___Fraction___Ideal Mean**
Or Perimeter

Sun__________0___________0________0____________0
Mercury______1___________3_____1/120______3.14 X10(7th)miles
Venus________2___________6______1/60______6.28
Earth________3___________9______1/40______9.42
Mars_________4__________12______1/30_____12.56
Ceres*_______8__________24______1/15_____25.13
Jupiter_____15__________45______1/8______47.12
Saturn______30__________90______1/4______94.24
Uranus______60_________180______1/2_____188.49
Neptune_____90_________270______3/4_____282.74
Pluto______120_________360______4/4_____376.99

*Ceres: prime representative of so-called "asteroids"

**means: adjusted for diameters of both bodies, sun and planet

In conclusion, I urge interested readers to review the detailed
heliocentric data and patterns pub lished in my earlier papers.
Perhaps someone can generate a full-scale computer analysis to
confirm why the sunspot cycle averages 22 years.

================================================================
Message 66 to Celestial-tuning@yahoogroups.com
From: Bill Arnold <billarnoldfla@y...>
Date: Tue Oct 1, 2002 11:52 pm
Subject: Re: ON THE SPECIAL THEORY OF ORDER

Norman Winski writes, "Martin, Have you read John Nelson's or Jane
Blizard's work on the correlation of planetary positions with Solar
activity? Please comment."

Martin writes, "the alignment of planets could not and does not
affect sunspot activity or the weather."

Gary Vezzoli writes, "Dear Bill -- The sun's tides are indeed very
small but not negligible, constituting about one-tenth the tidal
effect of the moon. The sun's effect of about 1 part in 10^8 is
still, I believe large enough to cause a change in the bond angle of
water, and can theoretically affect the DNA that it sheathes. Your
solar sunspot cycle work seems interesting and I would like to learn
more about your interpretations and hypothesis."

My paper "On the Special Theory of Order" cover pages 219 to 232,
Cycles Bulletin, Vol. XXXVI, No. 9, December 1985, with
illustrations, charts, and drawings, and here is the Table of
Contents and Abstract:

Table of Contents

I Abstract
II Introduction, Electro-Magnetic Nature of the Solar Wind
III Analysis of the Primary 22-Year Sunspot Cycle, See figure 1
IV Analysis of the Nile Flood Cycle, see Figure 1
V Analysis of the Secondary 100-Year Sunspot Cycle and the 100-Year

Weather Cycle, see Figure 1 and Schedule 1
VI Analysis of the Primary 22-Year Sunspot Cycle Nodes, see Schedule
1
VII Theory of a Special Order, see Figures 2, 3, 4 and 5
VII EMF (electro-magnetic force) Mechanism of a Galactic-Solar-
Planetary System Postulated, see Figure 6
IX Philosophical Considerations on an Ordered Galactic-Solar-
Planetary System
X Bibliography

I. ABSTRACT

On the Special Theory of Order postulates Order. It holds that the
physical laws of reality, known as "physics" in the realm of Science,
extend into deep space. Certainly, they extend from the center of
our own Milky Way galaxy to the center of our own Solar-Planetary
System, the Sun. A Special Order on a cosmic scale, as demonstrated
by this paper, is observed in the positive Correlation between the
Sunspot, the Weather and the Planetary Cycles. In a previous paper
on Solar-Planetary System Order (in CYCLES, "Bode's Law Explained,"
1979) this author demonstrated ordinal Proportionality between
planetary average distances from the Sun. In this present treatise,
when planetary synodic cycles are oriented to the Galactic-Solar Axis
(266-degrees to 86-degrees), a positive correlation is shown to exist
between these mechanical events and subsequent electro-magnetic data
observed in the Sunspot cycle and earthly Weather cycles. An emf
(electro-magnetic force) mechanism is postulated, and supported by
the work of Hale, Nicholson, Ellerman, Joy, Slurzberg and Osterheld,
Sheeley, Parker, Van Allen, Chambers, Nelson, Jones, Bray and
Loughead, and will account for the modulated cycle effects, supported
by the work of Dewey, Shirk, Jarvis, Ludwig, Eddy and Hand. The
Special Theory of Order about the mechanism of our Galactic-Solar
Planetary System with the planets acting as conductor-inductors
within the solar wind field when oriented to the Galactic center now
appears more evident, suggesing a Special Order from the Macrocosm
down to the micro.

__________________________________
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🔗Jon Szanto <JSZANTO@ADNC.COM>

10/11/2003 10:28:54 PM

Bill,

Please. You've been asked before: this is the *tuning* forum, and your topics and supporting data are *far* from the core of the subject matter of this forum. I salute you for the zeal with which you are involved in these subject areas, but it is a distraction from tuning, music, and tuning of music. Not to mention the umpteenth time we've seen "Arnold's Law".

Thanks in advance for trying to keep the list focused (as if it ever was...).

Cheers,
Jon

🔗Bill Arnold <billarnoldfla@yahoo.com>

10/11/2003 11:06:11 PM

Jon.

If it is a distraction, then *D-E-L-E-T-E* it.

I think I mentioned tuning at *least* once!

Bill

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> Bill,
>
> Please. You've been asked before: this is the *tuning* forum, and
your topics and supporting data are *far* from the core of the
subject matter of this forum. I salute you for the zeal with which
you are involved in these subject areas, but it is a distraction from
tuning, music, and tuning of music. Not to mention the umpteenth time
we've seen "Arnold's Law".
>
> Thanks in advance for trying to keep the list focused (as if it
ever was...).
>
> Cheers,
> Jon

🔗Carl Lumma <ekin@lumma.org>

10/11/2003 11:22:12 PM

>Jon.
>
>If it is a distraction, then *D-E-L-E-T-E* it.
>
>I think I mentioned tuning at *least* once!

Sorry Bill, your posts were way out of line. Please
don't post that stuff here!

-Carl

🔗monz <monz@attglobal.net>

10/12/2003 12:05:48 AM

hi Bill,

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > Jon.
> >
> > If it is a distraction, then *D-E-L-E-T-E* it.
> >
> > I think I mentioned tuning at *least* once!
>
> Sorry Bill, your posts were way out of line. Please
> don't post that stuff here!
>
> -Carl

i see that Bill has also put copies of his recent posts at

/celestial-tuning/

... which is what i expected. anyone who wants to continue
that thread may do so on the celestial-tunings list without
upsetting anyone. this kind of stuff is exactly what that
list is for.

-monz

🔗Gene Ward Smith <gwsmith@svpal.org>

10/12/2003 12:31:30 AM

--- In tuning@yahoogroups.com, "Bill Arnold" <billarnoldfla@y...>
wrote:
> Jon.
>
> If it is a distraction, then *D-E-L-E-T-E* it.

If you didn't post it in the first place--and you shouldn't have--he
would not need to delete it. Moreover, if he reads on the web, he
can't.

🔗Jon Szanto <JSZANTO@ADNC.COM>

10/12/2003 9:44:37 AM

Bill,

--- In tuning@yahoogroups.com, "Bill Arnold" <billarnoldfla@y...> wrote:
>
> If it is a distraction, then *D-E-L-E-T-E* it.

Deletion is not a problem, as someone else mentioned. It is a matter of improving the signal-to-noise ratio on a list. Even if you mention tuning, the general topic is quite far from the focus of this list, not to mention that the messages are cross-posted to lists of other subject areas. I'm sure that if you post a question that directly ties your cosmology into a direct question regarding tuning, it would not be as intrusive. As it is, the material - especially repeated postings of the same data - isn't germane to the vast majority of the list members.

Cheers,
Jon

🔗Bill Arnold <billarnoldfla@yahoo.com>

10/12/2003 6:17:36 PM

Hi, Jon.

I have read through your posts,
as well as others,
and you are way off-topic most of the time.

So who are you to talk?

A recent post pointed out that what I am
interested in and posted was about frequencies,
wavelengths, and all the relevant terms of this
list. But to please your narrow scoped mind I
will post *ONLY* to celestial-tuning, not to
tuning. No mas Bill to kick around. Enjoy
your narrow scoped mind, Jon. You won't learn
much about the world, but maybe that is *not*
your goal anyway.

Bill

=======================================================

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> Bill,
>
> --- In tuning@yahoogroups.com, "Bill Arnold" <billarnoldfla@y...>
wrote:
> >
> > If it is a distraction, then *D-E-L-E-T-E* it.
>
> Deletion is not a problem, as someone else mentioned. It is a
matter of improving the signal-to-noise ratio on a list. Even if you
mention tuning, the general topic is quite far from the focus of this
list, not to mention that the messages are cross-posted to lists of
other subject areas. I'm sure that if you post a question that
directly ties your cosmology into a direct question regarding tuning,
it would not be as intrusive. As it is, the material - especially
repeated postings of the same data - isn't germane to the vast
majority of the list members.
>
> Cheers,
> Jon

🔗Aaron K. Johnson <akjmicro@comcast.net>

10/12/2003 6:33:41 PM

On Sunday 12 October 2003 08:17 pm, Bill Arnold wrote:
> Hi, Jon.
>
> I have read through your posts,
> as well as others,
> and you are way off-topic most of the time.
>
> So who are you to talk?
>
> A recent post pointed out that what I am
> interested in and posted was about frequencies,
> wavelengths, and all the relevant terms of this
> list. But to please your narrow scoped mind I
> will post *ONLY* to celestial-tuning, not to
> tuning. No mas Bill to kick around. Enjoy
> your narrow scoped mind, Jon. You won't learn
> much about the world, but maybe that is *not*
> your goal anyway.
>
> Bill

Bill,

I would respectfully suggest that going slightly off topic on a subject that
was originally on topic doesn't count as "off topic" in the hard sense.
Deliberately instigating a topical thread in a newsgroup for which it wasn't
intended is. Sometimes people respond to a minor part of a thread and shoot
off a quick response. For example, in a hypothetical thread about west-coast
experimental music tuning styles, one might write "How about the governor's
race, eh?". And, another might respond, "yeah, Terminator...", which is
'off-topic', but part of the original thread, whose incipience was of a
purely music-tuning nature.

Granted, your point is taken, and too much of this needs to go to meta-tuning.

However, most of the time discussion concerns music-tuning related issues, not
general subjects in the cosmos that relate to frequency and wavelength, as
yours do. In my estimation, the goal of the group here is to discuss the
musical effects and aesthetics surrounding a given tuning, temperament, etc.,
even though the emphasis does sometimes get removed from the audible result,
and into the mathematics (which is part of the reason for the existence of
'tuning-math').

In any event, whether or not your subject may be of interest to those here,
calling a mailing-list user 'narrow scoped' is neither appropriate nor
welcome, given the purpose of this group; nor will it make you friends and
interested followers/converts, as apparently is your goal....

Respectfully,
Aaron.

> =======================================================
>
> --- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> > Bill,
> >
> > --- In tuning@yahoogroups.com, "Bill Arnold" <billarnoldfla@y...>
>
> wrote:
> > > If it is a distraction, then *D-E-L-E-T-E* it.
> >
> > Deletion is not a problem, as someone else mentioned. It is a
>
> matter of improving the signal-to-noise ratio on a list. Even if you
> mention tuning, the general topic is quite far from the focus of this
> list, not to mention that the messages are cross-posted to lists of
> other subject areas. I'm sure that if you post a question that
> directly ties your cosmology into a direct question regarding tuning,
> it would not be as intrusive. As it is, the material - especially
> repeated postings of the same data - isn't germane to the vast
> majority of the list members.
>
> > Cheers,
> > Jon
>
>
> You do not need web access to participate. You may subscribe through
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--
OCEAN, n. A body of water occupying about two-thirds of a world made
for man -- who has no gills. -Ambrose Bierce 'The Devils Dictionary'

🔗monz <monz@attglobal.net>

10/13/2003 12:24:52 AM

hi Aaron and Bill,

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>
wrote:

> Bill,
>
> I would respectfully suggest that going slightly off topic
> <etc.>

i wrote a very long and, IMO, one of the best posts i've
written recently, in response to this. i believe that it
gat zapped into the ether by the Yahoo web interface when
i tried to send it ... i don't see it appearing yet.
if so, then i am *EXTREMELY EXTREMELY* upset about this
stupid web interface.

anyway, there's no way i can try to rewrite it now.
so in case it never appears, i'll just sum up my opinion
that posts concerning cosmological "tuning" are acceptable
on this list if there are short and posted infrequently.

if one wants to post on that subject more comprehensively
and/or more often, the place to go is the Yahoo celestial-tuning
group.

/celestial-tuning/

and there was a lot in that post about list members acting
respectfully towards others too.

perhaps the main thing i can recall is this idea: if you
see a post to which you want to react negatively, use the
"count to 10 before responding" rule which helps people avoid
arguments. if the negative reaction hasn't subsided a bit
by then, then turn off the computer for an hour and go do
something else before responding.

i really do hope that other post finally comes thru,
but i think it probably won't .... :(

-monz

🔗monz <monz@attglobal.net>

10/13/2003 12:35:06 AM

i'm pretty sure it's gone forever. i remember the final line:

let's try to keep *harmony* on the *one* list where it
proably belongs more than any other in cyberspace!

and of course, i also made reference to my experiment in
composing sonic orerries of the movements of celestial
structures, as in these incipient versions of my
_Solar System_ piece:

http://sonic-arts.org/monzo/solarsystem/solar-system.htm

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> i wrote a very long and, IMO, one of the best posts i've
> written recently, in response to this. i believe that it
> gat zapped into the ether by the Yahoo web interface when
> i tried to send it ... i don't see it appearing yet.
> if so, then i am *EXTREMELY EXTREMELY* upset about this
> stupid web interface.
>
> anyway, there's no way i can try to rewrite it now.
> so in case it never appears, i'll just sum up my opinion
> that posts concerning cosmological "tuning" are acceptable
> on this list if there are short and posted infrequently.
>
> if one wants to post on that subject more comprehensively
> and/or more often, the place to go is the Yahoo celestial-tuning
> group.
>
> /celestial-tuning/
>
>
>
> and there was a lot in that post about list members acting
> respectfully towards others too.
>
> perhaps the main thing i can recall is this idea: if you
> see a post to which you want to react negatively, use the
> "count to 10 before responding" rule which helps people avoid
> arguments. if the negative reaction hasn't subsided a bit
> by then, then turn off the computer for an hour and go do
> something else before responding.
>
>
> i really do hope that other post finally comes thru,
> but i think it probably won't .... :(
>
>
>
> -monz

🔗francois_laferriere <francois.laferriere@oxymel.com>

10/13/2003 3:17:44 AM

> Thus occurs a great cosmic orchestration, ranging from the
microcosmic
> nuclear isotropicity -- directly undetectable by the human senses --
through
> the minuscule range detectable by humans, to the very complex
macrocosmic,
> supra-to-human-tunability symphonies of multiaggregates of
isotropically
> interpositioned galaxies."
> R. Buckminster Fuller

Amazingly, there are (relatively) recently discovered carbon molecules
that takes the form of little spheres, some of them (C60) soccer-ball
shaped. Those are named buckminsterfullerenes (or fullerenes for
short) because they are like the architectural structure invented by
Fuller.

Soccer ball shapes are everywhere in universe! Soccer Ball Shape rules
! let's create a cult to worship the Great Universal Soccer Ball shape!

... oups, this cult already exists worldwide (high priests are in Brazil).

:-)

François Laferrière

sorry for the noise generated, I couldn't resist

🔗Joseph Pehrson <jpehrson@rcn.com>

10/13/2003 9:55:11 AM

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

/tuning/topicId_47857.html#47900
>
> i really do hope that other post finally comes thru,
> but i think it probably won't .... :(
>
>

***This happens occasionally with me, too, on the Yahoo web
interface... Sometimes it asks me for my password and then the
message I have written is lost. So, whenever I do long, involved
posts, I also save them temporary to my wordprocessor and keep them
there until I'm absolutely sure that the message has been posted!

JP

🔗Gene Ward Smith <gwsmith@svpal.org>

10/13/2003 10:27:03 AM

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> ***This happens occasionally with me, too, on the Yahoo web
> interface... Sometimes it asks me for my password and then the
> message I have written is lost. So, whenever I do long, involved
> posts, I also save them temporary to my wordprocessor and keep them
> there until I'm absolutely sure that the message has been posted!

Have you tried using the back arrow on your browser? At one time this
didn't work for me, but it has been working now for some time.

🔗Joseph Pehrson <jpehrson@rcn.com>

10/13/2003 11:20:04 AM

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

/tuning/topicId_47857.html#47912

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > ***This happens occasionally with me, too, on the Yahoo web
> > interface... Sometimes it asks me for my password and then the
> > message I have written is lost. So, whenever I do long, involved
> > posts, I also save them temporary to my wordprocessor and keep
them
> > there until I'm absolutely sure that the message has been posted!
>
> Have you tried using the back arrow on your browser? At one time
this
> didn't work for me, but it has been working now for some time.

***Hi Gene,

Yes, of course, but the text was *gone* when I did that...

JP

🔗monz <monz@attglobal.net>

10/13/2003 11:59:21 AM

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> /tuning/topicId_47857.html#47900
> >
> > i really do hope that other post finally comes thru,
> > but i think it probably won't .... :(
> >
> >
>
> ***This happens occasionally with me, too, on the Yahoo web
> interface... Sometimes it asks me for my password and then
> the message I have written is lost.

yep, that's exactly what happened in my case.

> So, whenever I do long, involved posts, I also save them
> temporary to my wordprocessor and keep them there until
> I'm absolutely sure that the message has been posted!

yep, that's exactly what i should have done.

it really sucks that i wasn't careful to save it as
i composed it, because that was a great post.

-monz

🔗monz <monz@attglobal.net>

10/13/2003 12:02:07 PM

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> >
> > Have you tried using the back arrow on your browser?
> > At one time this didn't work for me, but it has been
> > working now for some time.
>
>
> ***Hi Gene,
>
> Yes, of course, but the text was *gone* when I did that...

of course i've tried that too, but it always brings me
back to the original "reply" setup, where the original
post is quoted but none of my response appears. so it's
useless.

-monz

🔗Carl Lumma <ekin@lumma.org>

10/13/2003 2:19:05 PM

>Amazingly, there are (relatively) recently discovered carbon molecules
>that takes the form of little spheres, some of them (C60) soccer-ball
>shaped. Those are named buckminsterfullerenes (or fullerenes for
>short) because they are like the architectural structure invented by
>Fuller.
>
>Soccer ball shapes are everywhere in universe! Soccer Ball Shape rules
>! let's create a cult to worship the Great Universal Soccer Ball shape!

First of all, soccer balls buckyballs are truncated icosahedra, not
dodecahedra. Weeks or whoever is really stretching it for the press.

-Carl

🔗Kurt Bigler <kkb@breathsense.com>

10/13/2003 3:41:21 PM

on 10/13/03 2:19 PM, Carl Lumma <ekin@lumma.org> wrote:

>> Amazingly, there are (relatively) recently discovered carbon molecules
>> that takes the form of little spheres, some of them (C60) soccer-ball
>> shaped. Those are named buckminsterfullerenes (or fullerenes for
>> short) because they are like the architectural structure invented by
>> Fuller.
>>
>> Soccer ball shapes are everywhere in universe! Soccer Ball Shape rules
>> ! let's create a cult to worship the Great Universal Soccer Ball shape!
>
> First of all, soccer balls buckyballs are truncated icosahedra, not
> dodecahedra. Weeks or whoever is really stretching it for the press.

Actually icosahedra and dodecahedra can be inter-morphed, by transforming
vertices into faces and faces into vertices. So my thought was that the
buckball is sort of a half-way point in the mortphing process, though I
didn't work out the details. But I found this web page that describes C60
generation as truncation of the icos by the dodec. But the operation used
to combine the two is actually a solid intersection, so the C60 is no more
icos than dodec, but truly a hybrid. The link:

http://www.geocities.com/CollegePark/9315/lw/tip5.htm

-Kurt

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> -Carl
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🔗Carl Lumma <ekin@lumma.org>

10/13/2003 4:18:55 PM

>Actually icosahedra and dodecahedra can be inter-morphed,
>by transforming vertices into faces and faces into vertices.

They are "duals".

>So my thought was that the buckball is sort of a half-way point
>in the mortphing process, though I didn't work out the details.

I think you can get an icosidodecahedron out of the intersection
of an icosahedron and a dodecahedron. It looks like if you make
the dodec a little bigger, you would indeed get a truncated
icosahedron.

All of these objects have icosahedral symmetry, and therefore
can be transformed into one another with various manipulations
fairly easily. But I don't think this reflects on the topologies
you get when you assume connectedness under them. If so, it is
a mistake to say the universe is connected "like a soccer ball".

-Carl