From: "frank zubek"

> >  'things' that are in *our* three-dimensional
> > world, then triangle is not the minimal "shape"
> > --tetrahedron is.
>
> > (Minor point: I said nothing about "regular.")
>
> O.K. well if you did not, than there is only one mite
> which is absolutelly the smallest one and that is a
> octane since this shape can not be reduced any
> further. Show me one shape which is smaller,( simpler,
> minimal).

What is an "octane?"
The only "octane" I know of is in gasoline....
A tetrahedron (in 3D) is the smallest possible "shape."
Is an "octane" a tetrahedron?

Peace
JB
jgbrawley@...
http://tetrahedraverse.com

John Brawley wrote:
> From: "frank zubek"
> What is an "octane?"

http://www.rwgrayprojects.com/synergetics/s04/figs/f1522.html
The above link at 415.22 top left are 8 1/8th-octahedra tets and i
belive are what Frank calls Octanes.

Please correct me if im incorrect about that Frank.

These 1/8th-octa tets are hte right angle ive spken of but never relaied
they existe in Synergetics.  Thankyou Frank for bring our attention to
these octanes.

Rybo

--- rybo6 <rybo6@...> wrote:
> John Brawley wrote:
> > From: "frank zubek"
> > What is an "octane?"
>
>
http://www.rwgrayprojects.com/synergetics/s04/figs/f1522.html
> The above link at 415.22 top left are 8
> 1/8th-octahedra tets and i
> belive are what Frank calls Octanes.
>
> Please correct me if im incorrect about that Frank.
>
> These 1/8th-octa tets are hte right angle ive spken
> of but never relaied
> they existe in Synergetics.  Thankyou Frank for
> bring our attention to
> these octanes.

Rybo

Now we talking, yes that's it. But it is the same
picture i have send you where you did inscribe the
cube in that tet. by the green lines.
>
frank

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--- John Brawley <jgbrawley@...> wrote:
> From: "frank zubek"
>
> > >  'things' that are in *our* three-dimensional
> > > world, then triangle is not the minimal "shape"
> > > --tetrahedron is.
> >
> > > (Minor point: I said nothing about "regular.")
> >
> > O.K. well if you did not, than there is only one
> mite
> > which is absolutely the smallest one and that is
> a
> > octane since this shape can not be reduced any
> > further. Show me one shape which is smaller,(
> simpler,
> > minimal).
>
> What is an "octane?"
> The only "octane" I know of is in gasoline....
> A tetrahedron (in 3D) is the smallest possible
> "shape."
> Is an "octane" a tetrahedron?
>
> Peace
> JB
> jgbrawley@...
> http://tetrahedraverse.com

Well now you know the other octane referring to a 1/8
of a octahedron, hence the suited name.And yes it is a
tet.

frank

>
>


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frank zubek wrote:

> http://www.rwgrayprojects.com/synergetics/s04/figs/f1522.html
> Now we talking, yes that's it. But it is the same
> picture i have send you where you did inscribe the
> cube in that tet. by the green lines.
> frank

Well Frank, im little confused, unclear and misunderstanding perhaps.

1) I thought you had said that the octane(tet) was a
derivative/dissection of tetrahedra but here above, if i understand  you
correctly, you seem to be saying that the Syn. graphic (415.22 above) is
correct in showing octanes(tets) but rather that they are actually
derivative of tets, ergo, they are 1/8th derivatives/dissections of
octahedra and;

2) I thought the blue graphic was a regular/symmetrical tet of which i
drew in the green cubic lines.  Whether or not that cube was just
illusionary or is still unclear in my mind.

I understand your rational of comparing elephants to this or that,  but
after seeing the above graphic in SYn.  im not as convinced in all of
your claims as i was previously.

Paste web site link again and any other graphics you might know of to
help enlighten us in and around your claims of most simple, more natural
etc..

Please and thanks Rybo

--- rybo6 <rybo6@...> wrote:
> frank zubek wrote:
>
> >
>
http://www.rwgrayprojects.com/synergetics/s04/figs/f1522.html
>
> > Now we talking, yes that's it. But it is the same
> > picture i have send you where you did inscribe the
> > cube in that tet. by the green lines.
> > frank
>
> Well Frank, im little confused, unclear and
> misunderstanding perhaps.
>
> 1) I thought you had said that the octane(tet) was a
>
> derivative/dissection of tetrahedra but here above,
> if i understand  you
> correctly, you seem to be saying that the Syn.
> graphic (415.22 above) is
> correct in showing octanes(tets) but rather that
> they are actually
> derivative of tets, ergo, they are 1/8th
> derivatives/dissections of
> octahedra and;
>
> 2) I thought the blue graphic was a
> regular/symmetrical tet of which i
> drew in the green cubic lines.  Whether or not that
> cube was just
> illusionary or is still unclear in my mind.
>
> I understand your rational of comparing elephants to
> this or that,  but
> after seeing the above graphic in SYn.  im not as
> convinced in all of
> your claims as i was previously.
>
> Paste web site link again and any other graphics you
> might know of to
> help enlighten us in and around your claims of most
> simple, more natural
> etc..
>
> Please and thanks Rybo

> http://clowder.net/zubek/zubek.html

Get to the picture of a octane and scrol down you will
see octane derived from a octahedron. I have newer
said it was derived from a reg. tet. However i said if
you put four octanes around a reg. tet. it will form a
cube. The large octane next to the small one is the
one picture i have send you previously and you
inscribed a cube in it which is exactly correct, there
is a cube mising one menber at the bottom which is not
vissible from that view.

In your previous message you said thanks frank to
bring my attention to it and now you saing that you
are not so sure about my claim, so now i'm confused
also. But the picture you have send is exactly the
same configuration i have.

frank


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--- rybo6 <rybo6@...> wrote:
> frank zubek wrote:
>
> >
>
http://www.rwgrayprojects.com/synergetics/s04/figs/f1522.html
>
> > Now we talking, yes that's it. But it is the same
> > picture i have send you where you did inscribe the
> > cube in that tet. by the green lines.
> > frank
>
> Well Frank, im little confused, unclear and
> misunderstanding perhaps.
>
> 1) I thought you had said that the octane(tet) was a
>
> derivative/dissection of tetrahedra but here above,
> if i understand  you
> correctly, you seem to be saying that the Syn.
> graphic (415.22 above) is
> correct in showing octanes(tets) but rather that
> they are actually
> derivative of tets, ergo, they are 1/8th
> derivatives/dissections of
> octahedra and;
>
> 2) I thought the blue graphic was a
> regular/symmetrical tet of which i
> drew in the green cubic lines.  Whether or not that
> cube was just
> illusionary or is still unclear in my mind.
>
> I understand your rational of comparing elephants to
> this or that,  but
> after seeing the above graphic in SYn.  im not as
> convinced in all of
> your claims as i was previously.
>
> Paste web site link again and any other graphics you
> might know of to
> help enlighten us in and around your claims of most
> simple, more natural
> etc..
>
> Please and thanks Rybo

> http://clowder.net/zubek/zubek.html

Get to the picture of a octane and scrol down you will
see octane derived from a octahedron. I have newer
said it was derived from a reg. tet. However i said if
you put four octanes around a reg. tet. it will form a
cube. The large octane next to the small one is the
one picture i have send you previously and you
inscribed a cube in it which is exactly correct, there
is a cube mising one menber at the bottom which is not
vissible from that view.

In your previous message you said thanks frank to
bring my attention to it and now you saing that you
are not so sure about my claim, so now i'm confused
also. But the picture you have send is exactly the
same configuration i have.

frank


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--- rybo6 <rybo6@...> wrote:
> frank zubek wrote:
>
> >
>
http://www.rwgrayprojects.com/synergetics/s04/figs/f1522.html
>
> > Now we talking, yes that's it. But it is the same
> > picture i have send you where you did inscribe the
> > cube in that tet. by the green lines.
> > frank
>
> Well Frank, im little confused, unclear and
> misunderstanding perhaps.
>
> 1) I thought you had said that the octane(tet) was a
>
> derivative/dissection of tetrahedra but here above,
> if i understand  you
> correctly, you seem to be saying that the Syn.
> graphic (415.22 above) is
> correct in showing octanes(tets) but rather that
> they are actually
> derivative of tets, ergo, they are 1/8th
> derivatives/dissections of
> octahedra and;
>
> 2) I thought the blue graphic was a
> regular/symmetrical tet of which i
> drew in the green cubic lines.  Whether or not that
> cube was just
> illusionary or is still unclear in my mind.
>
> I understand your rational of comparing elephants to
> this or that,  but
> after seeing the above graphic in SYn.  im not as
> convinced in all of
> your claims as i was previously.
>
> Paste web site link again and any other graphics you
> might know of to
> help enlighten us in and around your claims of most
> simple, more natural
> etc..
>
> Please and thanks Rybo
>
Here is the copy of your previous message i have
thought that we are clear least that was my assumption
from this message. So now i'm confused as why are you
doubting my claim.

frank

http://www.rwgrayprojects.com/synergetics/s04/figs/f1522.html
> The above link at 415.22 top left are 8
> 1/8th-octahedra tets and i
> belive are what Frank calls Octanes.
>
> Please correct me if im incorrect about that Frank.
>
> These 1/8th-octa tets are hte right angle ive spken
> of but never relaied
> they existe in Synergetics.  Thankyou Frank for
> bring our attention to
> these octanes.




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frank zubek wrote:
> --- rybo6 <rybo6@...> wrote:

>>http://clowder.net/zubek/zubek.html
> Get to the picture of a octane and scrol down you will
> see octane derived from a octahedron.

Ok. I think i get it now.  The blue large octane has the one vertex with
3  90-degree corners.  And it is the same as 1/8th-octahedra tet in Syn.
   link  above.  Does that sound correct?

So if that is now straight/clear/understood then next we ask what is the
octane(small?) derived from, if anything?  Maybe i thought you said that
it was derived/dissected from tet?

>I have newer
> said it was derived from a reg. tet. However i said if
> you put four octanes around a reg. tet. it will form a
> cube.

Ok, i got better understood now. :)

> The large octane next to the small one is the
> one picture i have send you previously and you
> inscribed a cube in it which is exactly correct, there
> is a cube mising one menber at the bottom which is not
> vissible from that view.

Yes the large octane, blue, has may have a potential cube within it.  Im
still convinced Frank.  Only being able to see from one view can be
deceiving to the eye.  There may be a cube there, but, i would to see it
from variable/many viewpoints graphically somehow.

> In your previous message you said thanks frank to
> bring my attention to it and now you saing that you
> are not so sure about my claim, so now i'm confused
> also. But the picture you have send is exactly the
> same configuration i have.
> frank


If you can help clarify (make clear) some of may questions stated in
this post will help.

Fullers "A" modules are from the tet and the "B" modules are from the
octahedron or is the "B" module is party from oct and from tet..  Maybe
that is the mite i forget.

Again ive been awake on all night shift and very tired, sorry for in
retardness/slowness on my part.  :(

Please do not be discourage by my comments.  I like where you going with
this i just want to see the path as walk along with you.  :)

Rybo

Hey Frank, You have been sending double and triple duplicate messages.
:)

Rybo

Alan, these were great links and graphics, however, i do not see any
kind of ico deriving from a snubbing/truncating a tet.

I forget if there were any other points we were discussing specifically.

Ry

Alan Michelson wrote:
> --- In synergeo@yahoogroups.com, rybo6 <rybo6@u...> wrote:
>
>>"Alan Michelson " wrote:
>>
>>
>>>The icosahedron is the snub tetrahedron.
>>
>>It is?  Hmmmm.  That would work well for my 8-UOI-GGF Matrix
>
>
> I did some soul- and web- searching for the answer, and I found:
> http://www.uwgb.edu/dutchs/symmetry/archpol.htm
> http://www.georgehart.com/virtual-polyhedra/symmetry_planes.html
> http://home.connexus.net.au/~robandfi/Stellations.html
>
> In addition, there is a Power-Point Presentation at
> http://www.math.nus.edu.sg/aslaksen/polyhedra/polyhedra.ppt
>
>
>
>
> To post a message, send plain text only to: synergeo@eGroups.com
> To Unsubscribe, send a blank message to: synergeo-unsubscribe@eGroups.com
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>
>

frank zubek wrote:
> --- rybo6 <rybo6@...> wrote:
>>Have you ever seen a tet with three 90 degree face
>>angles of its total 12?

> What you mean by total 12.

THe 1/8th-octa tets have 12 face/surface/opening angles just as all tets
do, however, the 1/8th-oct. tet has 3 face angles that are at 90 degrees
   i.e. three right triangles and fourth must be the isosceles you speak
of.  ???Hmm  ?

RY

Alan Michelson wrote:
> --- In synergeo@yahoogroups.com, rybo6 <rybo6@u...> wrote:
> What I mean is that the beams branch out like branches of tetrahedra.
> Many molecules branch out like that. For example: Diamonds and even
> water.

Cant see it but then im bushed/dead tired. Sorry :(


> That's what I thought, too! After all, an icosahedron is really a snub
> tetrahedron.

I would like you too point me to the graphics that show that.  Im skeptical.

Skewed(torqing) is the first step i.e. preceedes screwing(spiraling)

By the way Frank thats not to be confused with the English slang get
screwed.  :)  :)

RY

--- rybo6 <rybo6@...> wrote:
> frank zubek wrote:
> > --- rybo6 <rybo6@...> wrote:
>
> >>http://clowder.net/zubek/zubek.html
> > Get to the picture of a octane and scrol down you
> will
> > see octane derived from a octahedron.
>
> Ok. I think i get it now.  The blue large octane has
> the one vertex with
> 3  90-degree corners.  And it is the same as
> 1/8th-octahedra tet in Syn.
>   link  above.  Does that sound correct?

Yes;

> So if that is now straight/clear/understood then
> next we ask what is the
> octane(small?) derived from, if anything?  Maybe i
> thought you said that
> it was derived/dissected from tet?

Small octane is one single first order shape. Large
octane is the same thing just larger where you double
it's sides with, height where the volume eightoples.
It would be a two frequency octane. Notice that there
is eight cubes in a two frequency cube. There is eight
reg.tet. volumes in a large reg.tet.

> >I have newer
> > said it was derived from a reg. tet. However i
> said if
> > you put four octanes around a reg. tet. it will
> form a
> > cube.
>
> Ok, i got better understood now. :)
>
> > The large octane next to the small one is the
> > one picture i have send you previously and you
> > inscribed a cube in it which is exactly correct,
> there
> > is a cube mising one menber at the bottom which is
> not
> > vissible from that view.
>
> Yes the large octane, blue, has may have a potential
> cube within it.  Im
> still convinced Frank.  Only being able to see from
> one view can be
> deceiving to the eye.  There may be a cube there,
> but, i would to see it
> from variable/many viewpoints graphically somehow.

There is a cube, as you have inscribe it correctly.

> > In your previous message you said thanks frank to
> > bring my attention to it and now you saing that
> you
> > are not so sure about my claim, so now i'm
> confused
> > also. But the picture you have send is exactly the
> > same configuration i have.
> > frank
>
>
> If you can help clarify (make clear) some of may
> questions stated in
> this post will help.
>
> Fullers "A" modules are from the tet and the "B"
> modules are from the
> octahedron or is the "B" module is party from oct
> and from tet..  Maybe
> that is the mite i forget.

I think you have it wrong here. The A-B- mods are
derived both from a quorter 1/4 reg.tet. There is
three left and three right oriented shapes, same as
A-B- mods. 24 all together in a whole reg.tet.

> Again ive been awake on all night shift and very
> tired, sorry for in
> retardness/slowness on my part.  :(

No appologie necessary, it is my limited writing
skills draging you through my mambo-jumbo.

  > Please do not be discourage by my comments.  I like
> where you going with
> this i just want to see the path as walk along with
> you.  :)

frank

> Rybo
>
>


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--- rybo6 <rybo6@...> wrote:
> Hey Frank, You have been sending double and triple
> duplicate messages.
> :)
>
> Rybo
>
> I have no idea why is this happening I had this
problem before but it is not me, least i'm not aware
that i'm doing someting wrong.

frank

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--- rybo6 <rybo6@...> wrote:
> frank zubek wrote:
> > --- rybo6 <rybo6@...> wrote:
> >>Have you ever seen a tet with three 90 degree face
> >>angles of its total 12?
>
> > What you mean by total 12.
>
> THe 1/8th-octa tets have 12 face/surface/opening
> angles just as all tets
> do, however, the 1/8th-oct. tet has 3 face angles
> that are at 90 degrees
>   i.e. three right triangles and fourth must be the
> isosceles you speak
> of.  ???Hmm  ?

O.K. i understand the 12 face openings but just think
what are you saing now if this is a 1/8 of a
octahedron which is made up by octanes and all the
faces you see in a octahedron are all equilateral tri,
than a octane must have a equilateral tri. at it's
base. Isosceles tri. are the blue ones consit of a 90
deg. and two 45 deg. angles. I have sent you a picture
of that tri.

frank
> RY
>
>


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(JBw)
> > What is an "octane?"
> > The only "octane" I know of is in gasoline....
> > A tetrahedron (in 3D) is the smallest possible
> > "shape."
> > Is an "octane" a tetrahedron?

> Well now you know the other octane referring to a 1/8
> of a octahedron, hence the suited name.And yes it is a
> tet.

Ok so you're saying an octane is the smallest possible 3D "shape" and I'm
saying a tet is the smallest possible 3D "shape" and a tet is an octane and
an octane is a tet so we're saying the same thing.

(Proprietary-'special' names for things which already have perfectly good
names merely draws confusion into places it needn't be.)


Peace
JB
jgbrawley@...
http://tetrahedraverse.com

--- John Brawley <jgbrawley@...> wrote:
> (JBw)
> > > What is an "octane?"
> > > The only "octane" I know of is in gasoline....
> > > A tetrahedron (in 3D) is the smallest possible
> > > "shape."
> > > Is an "octane" a tetrahedron?
>
> > Well now you know the other octane referring to a
> 1/8
> > of a octahedron, hence the suited name.And yes it
> is a
> > tet.
>
> Ok so you're saying an octane is the smallest
> possible 3D "shape" and I'm
> saying a tet is the smallest possible 3D "shape" and
> a tet is an octane and
> an octane is a tet so we're saying the same thing.

John, tet. is a minimal shape of four sides no
argument there i was saying which if any can be
considered as absolutely the most minimal shapes of
all mites. It is here where i can say that from a
general term as mite there may be one which is the
smallest of all (minimal) shapes. As is it true for a
reg.tet. to be the smallest from all the symmetrical
shapes. Cone as the largest fractional shape and
sphere as the largest of all shapes.

> (Proprietary-'special' names for things which
> already have perfectly good
> names merely draws confusion into places it needn't
> be.)
>
John, i did not invented the name i have read about it
somewhere and it was a name which suited the purpose.
All other shapes in my polyhedra have the names i have
give them since it was my invention. Of course if
there is a name which is already established i
definitely agree that new names just add to the
confusion. But octane obviously does not have a name
other than 1/8 of a octahedron and i used to call it
as it is documented in my writing a "three sided
pyramid".
Names are best if they are short and for practical
purposes have the name which are best suited for it's
appearance or some fundamental function.

frank


>
> Peace
> JB
> jgbrawley@...
> http://tetrahedraverse.com
>
>
>


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frank zubek wrote:

> Small octane is one single first order shape. Large
> octane is the same thing just larger where you double
> it's sides with, height where the volume eightoples.
> It would be a two frequency octane.

Gottcha.  They are both i/8-octa tets(octanes).  Geometrically identical.

> Notice that there
> is eight cubes in a two frequency cube. There is eight
> reg.tet. volumes in a large reg.tet.

Is there picture of this in SYn.  Do you hav a copy of Syn. 1 & 2 Frank?



> I think you have it wrong here. The A-B- mods are
> derived both from a quorter 1/4 reg.tet. There is
> three left and three right oriented shapes, same as
> A-B- mods. 24 all together in a whole reg.tet.

I think you partly correct.  "A" mods are in th quarter tets but "B"
mods are wholy or partly associtated with oct.  Im too tired to get book
and search now.

> No appologie necessary, it is my limited writing
> skills draging you through my mambo-jumbo.

I think youre doing ok.  What is your primary language?

I am sleep deprived i.e. slepp deprivated. :)

RY

frank zubek wrote:
> O.K. i understand the 12 face openings but just think
> what are you saing now if this is a 1/8 of a
> octahedron which is made up by octanes and all the
> faces you see in a octahedron are all equilateral tri,
> than a octane must have a equilateral tri. at it's
> base. Isosceles tri. are the blue ones consit of a 90
> deg. and two 45 deg. angles. I have sent you a picture
> of that tri.


Hmmm? Need Syn. graphic.  I saw one but cant get there now.  Maybe you
can send the SYn. link

RY

--- rybo6 <rybo6@...> wrote:
> frank zubek wrote:
>
> > Small octane is one single first order shape.
> Large
> > octane is the same thing just larger where you
> double
> > it's sides with, height where the volume
> eightoples.
> > It would be a two frequency octane.
>
> Gottcha.  They are both i/8-octa tets(octanes).
> Geometrically identical.
>
> > Notice that there
> > is eight cubes in a two frequency cube. There is
> eight
> > reg.tet. volumes in a large reg.tet.
>
> Is there picture of this in SYn.  Do you hav a copy
> of Syn. 1 & 2 Frank?
>
>No i do not, but both immages are depicted on the web
page about elusive cube of mine.
>
> > I think you have it wrong here. The A-B- mods are
> > derived both from a quorter 1/4 reg.tet. There is
> > three left and three right oriented shapes, same
> as
> > A-B- mods. 24 all together in a whole reg.tet.
>
> I think you partly correct.  "A" mods are in th
> quarter tets but "B"
> mods are wholy or partly associtated with oct.  Im
> too tired to get book
> and search now.

Maybe one can construct a octahedron or coupler or
cube by strictly via A or via B mod but in 1/4 reg.
tet. i see shapes of right and left hand oriented
sugesting A-B mod. but i may be wrong since i my self
i'm not much familiar with it.

> No appologie necessary, it is my limited writing
> > skills draging you through my mambo-jumbo.
>
> I think youre doing ok.  What is your primary
> language?

I'm from Slovakia old name for Czechoslovakia may be
more familiar to you.
>
> I am sleep deprived i.e. slepp deprivated. :)
>
> RY
>
frank
>


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--- rybo6 <rybo6@...> wrote:
> frank zubek wrote:
> > O.K. i understand the 12 face openings but just
> think
> > what are you saing now if this is a 1/8 of a
> > octahedron which is made up by octanes and all the
> > faces you see in a octahedron are all equilateral
> tri,
> > than a octane must have a equilateral tri. at it's
> > base. Isosceles tri. are the blue ones consit of a
> 90
> > deg. and two 45 deg. angles. I have sent you a
> picture
> > of that tri.
>
>
> Hmmm? Need Syn. graphic.  I saw one but cant get
> there now.  Maybe you
> can send the SYn. link
>
> RY
>
> Isc. right. deg. triangle is the triangle of two
identical *lenght* legs meeting at 90 deg.forming 45
deg. at both side of the base which is a hypotenuse of
that triangle. I have send the picture to you before
on a previous messige. All three triangles used in my
set are depicted on the web page i have sent to you
regarding the elusive cube.
>
frank


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frank zubek wrote:
  >
  > No not at all, i just send the picture reffereing to
  > the star tet. immage you were posting; and yes i
  > reallize that there is a cube with in a octane.

Hi Frank
Well that is cool if a cube is in a tet(octane). Ive never sen that before.

Have you ever seen a tet with three 90 degree face angles of its total 12?

  > No not at all, i just know that you tend to make
  > connections from a observations and some are
  > deffinitelly revolutionary if they are correct.

Yeah lots of speculation coming from this neck of the woods. :)

  > Sure you are absolutelly correct, English is my third
  > language and many times i do tend to chose the wrong
  > word but the meaning is the same. I do not like very
  > ellaborate skillfully crafted words i prefer
  > simplicity

Well i meanttechnically correct, but, as you may have noticed i then
changed my mind/thoughts and thought it didnt make any differrence
technically either, once i realized that as long as whatever word is
used is referenced to the word "shape" --as you did-- because
shape(spiral,circle,etc.) like "angle" is likened to pattern which is
not related to size/time/mesurement ergo as Fuller says about angle and
wave it "shape" is a metaphysical(pre-frequency)   -aas you sate below--
concept/idea.  Does that make sense?  Do those termiologies seem equal
or nearly equal in content or whatever?

  > Who is George?

It is an american saying "yes, by George i belive it is raining today"
and now i have no idea were that saying orignates from.  Ive never heard
it said "no, by George" now that i think about it.

  > Shape is prefrequency as stated by Kirby and size is
  > apparent at the particular frequency only but once
  > again it is because evrybody is stucked on Fullers
  > concept and thinking.

Yes, pre-time-size.

  > Just by comparing my dissections with  Fullers it is
  > obvious and i call his dissections induced seaking a
  > unity by induced (forced)dissections arriving at all
  > identical irregular shapes. In my dissections i have
  > fallowed a natural order. I have arrived at same
  > volumes by different shapes.

Hmm that is interesting.  Fuller always felt like he was following
natures path in many of his ways of being.

Please elaborate on how your path may be more natural and less induced.


  > I'm not sure about the speling but you have seen the
  > octane and i talking about the blue triangles making
  > up it's faces.

Can you make a drawing of a few diffrrent trinagle types and compare
them to your octanes surface isoceles triangles for us?


  > I'm not sure what you mean here, a two freq. octane
  > has it's corners made up by those triangles.

It may be that your octane is just the tet ive often wondered about but
never took time to locate, build or draw etc.  COOL!


  > Octane is 1/8 of a octahedron. Four of these arround a
  > reg. tet. form a cube.

IS there a picture in Syn. or elswhere to help make it obvious?

  >
  > Look, if i dissect a reg. tet. removing four identical
  > tets.from every corner the remaining core contains a
  > octahedron. If i remove identical shapes from each
  > corner (1/2 octahedrons) the remaining shape is a
  > cubota hedron. If i would continue by the rules of
  > corners than after a cubotahedron i may end up with a
  > icosa or dodeca i'm not sure but i'm sure that
  > eventually i end up with a sphere cosist of small
  > equilateral triangles. In other words the more you cut
  > the larger the remainer is in *relative sense*

Yes it does seem true that if you continually truncate the edges of any
polyhedron you are rounding it off --"like ocean surf does to
sand{Fuller}"-- and makes the polyhedron more rounded/spherical.


  > Kirby, Fuller,Anderson and all others think that a A-B
  > mod is the smallest since it is derived from the
  > smallest symetrical shape. But that is nothing else as
  > to say that if your familly is consist of 8 members
  > and mine is only consist of four members that it makes
  > me twice is larger than you.

Yes, i follow you logic and it makes perfect sense to me.  Im just a slow
learner whose is not good at math and than God{des} for all the pictures
in Synergetics or most of us would really be "up a tree" i.e. going
whacko trying to figure it all out.


  > Actually not really as a matter of fact it is the
  > least interesting and the least appealing shape to me,
  > but by examining my dissections i have just realize
  > that even if i try no matter how hard i can not mamage
  > to make a smaller (minimal)shape. Further more in my
  > cuts there is three times is much octane's than any
  > other shape. Octane in my set is the most practical
  > and essential in all connections of larger shapes. It
  > is like a hyd. atom being the smallest and everywhere.

Hmm, Cool!  If you can practice putting this into words of explanation
with some associted graphics i think we could all pass some judgements
on your work. <Smile>  :)

Really tho, it is a cool thing you seem to be discovering.You may become
the Synergeo Synergetic Natrualpath(SSN), or leutintant, president. Ken
is the Synergeo Syenrgetic Housemom(SSH) I say Kirby is the Synergeo
Synegetic Master(SSM) Ive semi-elected myself as the Synergeo Synergetic
General (SSG), JB is the Synergeo Synergetic Antagonist(SSA), Tom is the
SYnergeo Synegetic Watchdog(SSW),Dick is the Synergeo Synergetic
Conehead (SSC)  --no offense DF--;)

  > Yes i have but he as others are shy to confirm
  > something new, he can not argue it or to show me a
  > smaller shape. All they concept is true if you
  > consider a fractional shape as a member of the whole
  > but i'm talking shapes independent of the larger
  > whole. I'm talking shape on it's own and in that
  > regard no one have showed me a smaller shape.

I want to hear more on this. Hope we can get more viepoints.

  > I wish he was alive and he could see my dissections
  > and reasoning. Fuller ofcourse is right in that, that
  > he forsfully disected a reg. tet. in to identical
  > shapes being than the smallest unit of a reg. tet. But
  > try to immagine a A-B mod. having it's shortest edge
  > of one unit lenght and you will see that the A-B. mod
  > will be larger. First order cube made up by A-B mods
  > would have 9 shapes in a cube and this is a problem in
  > nature where such cube could not be divided in to 1/2.
  > By building the wall his cube would be way larger than
  > mine. This is a such a simple statement that most
  > folks not consider it's validity, because it comes
  > from nobody like me.

If what you say has validity, and i think it does, and if we were to
follow in the same avenue of specualtive associations between geometry
and cosmic particles as Fuller has done then where he has the quarks
being the A's or Bs' or both, i forget which, then perhaps if your 1/8th
tets come into threes similar too Fullers, then they too may fit the
"bill"/profile for being quarks.


  > Well i can not do that since my concept is independen
  > from a concentric heirarchie my concept deals with a
  > shapes as a individuals and not as a members of the
  > whole.

No whole?  Holy mackeral good buddy!  There has got to be a whole <smile>
It is un-holy for you not to have some kind of whole in your octane
matrix (OM)

  >
  > These are Kirby's words all true no dispute but in
  > absolute truth seeking the smallest and the largest of
  > shapes conc. heir. deals with the whole continium of
  > systems.
  > In synergetics, shape is prefrequency.  Size enters
  > the
  > picture with frequency, at which point we have a
  > spectrum
  > of smallest to largest -- but the same shape may
  > appear
  > at any frequency

Im tired once again.  But your approach i think is worth of more
consideration, being perhaps more natural than Fullers.

  > There is one more thought which i have also tried just
  > very surface observation. If i dissect any tet, and
  > keep dissecting, so far i have always come to the same
  > conclussion that all dissections eventually arrive at
  > the origin of the same shape. From seemingly a chaotic
  > order of cuts the chaos becomes equivalent. I maybe be
  > able to prove that all dissections will eventually
  > arrive at the smallest building block of nature and it
  > will not be a A-B or T mod. but a octane and the whole
  > comedy ends up where it all started.

Hmmm.  Doesnt this depend on you do your dissections?  Cleavging via
axis spinning?  What axis develop with octane matix?  I think FUller
only discusses two types of axis spinning for tet

Parrallel and perpendicular.  If there are more Kirby is the man to ask.
He knows synergetics better thtn anyone i know.

RYbo

I have done an EIG project of which there
are two screen shots at.

http://users.highway1.com.au/~dharmraj/gallery/oneivm.html

There is a link to the program which is used
for viewing and creating EIG's. The program is named
Springdance and an EIG is a file from that program. It
allows building of synergetic geometry.

This project was done by building a four frequency tet and
then constructing a rhombic dodecahedral mite core at the
center. Then out at each corner of the four frequency tetI constructed
a rhombic dodecahedral cores around a tet center and an oct center.

dharmraj

--- In synergeo@yahoogroups.com, rybo6 <rybo6@u...> wrote:
> Alan, these were great links and graphics, however, i do not see
> any  kind of ico deriving from a snubbing/truncating a tet.

Then you should have seen:
http://www.google.com/search?q=snub+tetrahedron+is+icosahedron
That's what the results say!

> I forget if there were any other points we were discussing
> specifically.

Molecular structures in
http://groups.yahoo.com/group/synergeo/message/10361

Gaps in the ball at
http://groups.yahoo.com/group/synergeo/message/10338

> Alan Michelson wrote:
> >
> > I did some soul- and web- searching for the answer, and I found:

> > http://www.uwgb.edu/dutchs/symmetry/archpol.htm
Near the bottom it says, "Thus, a snub tetrahedron is an icosahedron."

> > http://www.georgehart.com/virtual-polyhedra/symmetry_planes.html
At "The Planes of Symmetry of the Tetrahedron", George Hart says that
"a snub tetrahedron can be thought of as a three-colored icosahedron"
He also has a glossary at:
http://www.georgehart.com/virtual-polyhedra/glossary.html

> > http://home.connexus.net.au/~robandfi/Stellations.html
In case study #1: "icosahedron, which may be thought of as a snub
tetrahedron."

> > In addition, there is a Power-Point Presentation at
> > http://www.math.nus.edu.sg/aslaksen/polyhedra/polyhedra.ppt
Near the end of that Power Point presentation, you see a question:
"Why no snub tetrahedron?"
The answer to the snub tetrahedron:
"It's the icosahedron!"

> --- John Brawley <jgbrawley@...> wrote:
> > Ok so you're saying an octane is the smallest
> > possible 3D "shape" and I'm
> > saying a tet is the smallest possible 3D "shape" and
> > a tet is an octane and
> > an octane is a tet so we're saying the same thing.
>
> John, tet. is a minimal shape of four sides no
> argument there i was saying which if any can be
> considered as absolutely the most minimal shapes of
> all mites. It is here where i can say that from a
> general term as mite there may be one which is the
> smallest of all (minimal) shapes. As is it true for a
> reg.tet. to be the smallest from all the symmetrical
> shapes. Cone as the largest fractional shape and
> sphere as the largest of all shapes.

Well, let's look at this in reductionist methodology:
Start with a tet --any tet, any irregularity, any size.
Now, to reduce the size, you reduce the length of an edge (any edge).
This enebles you to keep on reducing edge lengths, one edge at a time,
always (I suggest) reducing the longest edge.
I put it to you that this process, if carried out logically to its extreme,
will inevitably end you up with a (very, very tiny) *regular* tet, since to
have an edge longer than the others means you can reduce it, no matter which
edge is longer, so that in the "infinite fullness" of this process you end
up with a regular tet--all edges equal.

IN other words, no matter how irregular the tet with which you start, you'll
end up with the regular one.

Now, IF you restrict your argument to ONLY "mites," then of course you
"pre-define" the tet as irregular, but so what have you done?  You can
either say a *mite* is the smallest *mite* (in which case you say nothing in
general about tets), or you can say some specific (but unspecified) *mite*
is the smallest possible *tet*, in which case I think you're wrong since
mites are by definition (?) IRregular tets.
Peace
JB
jgbrawley@...
http://tetrahedraverse.com









>
> > (Proprietary-'special' names for things which
> > already have perfectly good
> > names merely draws confusion into places it needn't
> > be.)
> >
> John, i did not invented the name i have read about it
> somewhere and it was a name which suited the purpose.
> All other shapes in my polyhedra have the names i have
> give them since it was my invention. Of course if
> there is a name which is already established i
> definitely agree that new names just add to the
> confusion. But octane obviously does not have a name
> other than 1/8 of a octahedron and i used to call it
> as it is documented in my writing a "three sided
> pyramid".
> Names are best if they are short and for practical
> purposes have the name which are best suited for it's
> appearance or some fundamental function.
>
> frank
>
>
> >
> > Peace
> > JB
> > jgbrawley@...
> > http://tetrahedraverse.com
> >
> >
> >
>
>
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>

Alan Michelson wrote:
> Then you should have seen:
> http://www.google.com/search?q=snub+tetrahedron+is+icosahedron
> That's what the results say!

Ok, you are correct!  I rea the text this time and see that snub tet
becomes and irregular icosahedron with no face trianlges ergo no
circumferential structure.  If i ever find my polyhedral sheet i think
that snub tet is on it.  Thanks for bring it to our attention ar
synergeo.  We are much more informed now.

Here is link to one of Syn's  of tet ico overlay-like graphic.
In reference to this photo FUller says that four of ico's tringles are
parallel to four faces of tet that leaves 16 unaccountef for in relation
to the tet.  Fuller says in caption that ico is skew to the tet.

Another 8 of icos triangles are parrallel to the oct.  This is important
to Jim Lehmans PVM/LVM which clos packs icosahedra with irregular oct's
and an irregular rhombocubohedron(?)

http://www.uwgb.edu/dutchs/graphic1/polyhedr/arpoltil.gif

> Molecular structures in
> http://groups.yahoo.com/group/synergeo/message/10361

Skewed in relation to another polyheron it may be overlayed with

> Gaps in the ball at
> http://groups.yahoo.com/group/synergeo/message/10338

Dihedral angles.  Not sure wee to go with that.


Thanks again Alan.

--- John Brawley <jgbrawley@...> wrote:
>
> > --- John Brawley <jgbrawley@...> wrote:
> > > Ok so you're saying an octane is the smallest
> > > possible 3D "shape" and I'm
> > > saying a tet is the smallest possible 3D "shape"
> and
> > > a tet is an octane and
> > > an octane is a tet so we're saying the same
> thing.
> >
> > John, tet. is a minimal shape of four sides no
> > argument there i was saying which if any can be
> > considered as absolutely the most minimal shapes
> of
> > all mites. It is here where i can say that from a
> > general term as mite there may be one which is the
> > smallest of all (minimal) shapes. As is it true
> for a
> > reg.tet. to be the smallest from all the
> symmetrical
> > shapes. Cone as the largest fractional shape and
> > sphere as the largest of all shapes.
>
> Well, let's look at this in reductionist
> methodology:
> Start with a tet --any tet, any irregularity, any
> size.
> Now, to reduce the size, you reduce the length of an
> edge (any edge).
> This enebles you to keep on reducing edge lengths,
> one edge at a time,
> always (I suggest) reducing the longest edge.
> I put it to you that this process, if carried out
> logically to its extreme,
> will inevitably end you up with a (very, very tiny)
> *regular* tet, since to
> have an edge longer than the others means you can
> reduce it, no matter which
> edge is longer, so that in the "infinite fullness"
> of this process you end
> up with a regular tet--all edges equal.
>
> IN other words, no matter how irregular the tet with
> which you start, you'll
> end up with the regular one.
>
> Now, IF you restrict your argument to ONLY "mites,"
> then of course you
> "pre-define" the tet as irregular, but so what have
> you done?  You can
> either say a *mite* is the smallest *mite* (in which
> case you say nothing in
> general about tets), or you can say some specific
> (but unspecified) *mite*
> is the smallest possible *tet*, in which case I
> think you're wrong since
> mites are by definition (?) IRregular tets.
> Peace
> JB
> jgbrawley@...
> http://tetrahedraverse.com
>
Yes, the process described above is somewhat
interesting but it is not the one i was considering.
I realize according to my cuts that the more one cuts
by the rules of vertexis (corners) as i have applied
in my dissections it was obvious that more i cut the
more larger the leftover is going to be in *relative *
sense. Remove the cube corners and you end up with a
reg. tet. remove it's corners and you end up with a
octahedron remove it's corners and you end up with a
cubotahedron and than maybe with a icosahedron and
than with dodeca hadron and eventually you end up a
spherical structure consist of a infinitely small
equilateral triangles all over it's surface.

Maybe I'm wrong but this is the result i see so far.
If i apply the same rule to a *mite* and i have try
this to some level i always end up with the shape i
have started with at the beggining. I just thinking
that to continue this process may eventually will end
with a 1/8 octahedron. I doubth that it will end with
a reg.tet. since this tet. is made up by the longest
of lines i think it will end up with something smaller
more elementary and fundamental. It is the structure
of a octahedron it's self which is reduced to all
identical shapes the smallest and the strongest of all
shapes.

John, i do realize that it may be all wrong, but it is
worth to consider especially if no one has try this to
such level. If someone already have, well than it may
already bin proven, that my resuarche leads to
nowhere.

Now if i would build the wall by the smallest of
shapes it is obvious that such block would have to be
a tet. In my case it would be a octane (1/8 octhed).
If no block can have any edge shorther than one unit
than it appears that even a Q- mod or T- mod or any
sprite, rite, bite or what ever would have its surface
areas somewhat larger than the 1/8 octahedran.

I think it's worth the investigation before one Shu
t's it down with out any deeper cosideration.

frank





>
>
>
>
>
>
>
>
> >
> > > (Proprietary-'special' names for things which
> > > already have perfectly good
> > > names merely draws confusion into places it
> needn't
> > > be.)
> > >
> > John, i did not invented the name i have read
> about it
> > somewhere and it was a name which suited the
> purpose.
> > All other shapes in my polyhedra have the names i
> have
> > give them since it was my invention. Of course if
> > there is a name which is already established i
> > definitely agree that new names just add to the
> > confusion. But octane obviously does not have a
> name
> > other than 1/8 of a octahedron and i used to call
> it
> > as it is documented in my writing a "three sided
> > pyramid".
> > Names are best if they are short and for practical
> > purposes have the name which are best suited for
> it's
> > appearance or some fundamental function.
> >
> > frank
> >
> >
> > >
> > > Peace
> > > JB
> > > jgbrawley@...
> > > http://tetrahedraverse.com
> > >
> > >
> > >
> >
> >
> > __________________________________________________
> > Do you Yahoo!?
> > Yahoo! Mail Plus - Powerful. Affordable. Sign up
> now.
> > http://mailplus.yahoo.com
> >
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> >             ADVERTISEMENT
> >
> >
> >
> >
> > To post a message, send plain text only to:
> synergeo@eGroups.com
> > To Unsubscribe, send a blank message to:
> synergeo-unsubscribe@eGroups.com
> >
> > Your use of Yahoo! Groups is subject to the Yahoo!
> Terms of Service.
> >
> >
>
>


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--- In synergeo@yahoogroups.com, frank zubek <fzubek@y...> wrote:

> I realize according to my cuts that the more one cuts
> by the rules of vertexis (corners) as i have applied
> in my dissections it was obvious that more i cut the
> more larger the leftover is going to be in *relative *
> sense. Remove the cube corners and you end up with a
> reg. tet. remove it's corners and you end up with a
> octahedron remove it's corners and you end up with a
> cubotahedron and than maybe with a icosahedron and
> than with dodeca hadron and eventually you end up a
> spherical structure consist of a infinitely small
> equilateral triangles all over it's surface.

This is very interesting.

Maybe  drop the "infinitely small equilateral"  part. It is suffient , I think,
to say
that there will be only triangles all over the surface. It will always be
faceted.

I don't think symmetry or  shape of the triangles matters in the general case.
But do count vertexes, vectors and openings. Apply Euler.

Dick

--- In synergeo@yahoogroups.com, rybo6 <rybo6@u...> wrote:
> Here is link to one of Syn's  of tet ico overlay-like graphic.
> In reference to this photo FUller says that four of ico's tringles
> are
> parallel to four faces of tet that leaves 16 unaccountef for in
> relation
> to the tet.  Fuller says in caption that ico is skew to the tet.
>
> Another 8 of icos triangles are parrallel to the oct.  This is
> important
> to Jim Lehmans PVM/LVM which clos packs icosahedra with irregular
> oct's
> and an irregular rhombocubohedron(?)

Any eight of the icosahedron's triangles can be parallel to the
octahedron's triangles. Of these eight triangles, every other triangle
is parallel to a tetrahedron's triangle. In fact, in
http://groups.yahoo.com/group/synergeo/message/10326
I said that, "The dihedral angle between the faces of a regular
tetrahedron is 1.230959418 radians or 70.52877938 degrees. This is
also the angle between alternating faces of a regular octahedron."
If you extend the alternating faces of a regular octahedron, then you
get a regular tetrahedron. See the double tetrahedron in
http://georgehart.com/virtual-polyhedra/figs/so.gif
and you will see that each tetrahedron supplies the alternating faces
in the inner octahedron.

> http://www.uwgb.edu/dutchs/graphic1/polyhedr/arpoltil.gif

Great comparisons with three-, four-, and six- fold tilings! I think
of these as infinite polyhedra. Now see if we can tile the polyhedra
in three dimensions (i.e. sphere packing). If not, perhaps they wrap
to a fourth dimension? I know that five-fold symmetry tends to be the
odd-ball, I mean gap-ball here. But the golden mean is based on the
simple equation (x*x)±x-1, in other words, the external proportion
is the same as the internal proportion. That's why it's so pleasing in
nature.

> > Gaps in the ball at
> > http://groups.yahoo.com/group/synergeo/message/10338
>
> Dihedral angles.  Not sure wee to go with that.

I just did; see above!

> Thanks again Alan.