Platonic Solids

[RealiDan@...]

hi,

i was wondering if there is a post here or elsewhere that gives the
diameter of each of the spheres of the nested platonic solids. say
the first (inside) isocohedron diameter is set to 1, what would be
the diameter of each of the successive spheres as the solids
transform? thanks.

danny

[Jeremy Weiland]

> i was wondering if there is a post here or elsewhere
> that gives the diameter of each of the spheres of
> the nested platonic solids. say the first (inside)
> isocohedron diameter is set to 1, what would be
> the diameter of each of the successive spheres as
> the solids transform? thanks.

well, let me venture a guess. if you're moving a
sphere from one octave to the next highest, you're
doubling the frequency. if we assume that the
diameter of that sphere would likewise be doubled,
then that would mean that each nested platonic solid
that envelops the smaller sphere would be a seventh of
the original diameter doubled, or if d0 is the
diameter of the smaller, original sphere, the
"diameter" (you can't have a diameter of anything but
a circle, but we can think of it as ratio of size) of
any given enveloping shape would be x, where:

x = (2d * (n/7))+d, where n is the number of the solid
(the octahedron would be three, tetrahedron four, cube
five, etc.)

in any case, no matter what platonic solid you would
start with, the next shape would be (2d)/7 bigger than
the original, or (((2d)/7) + d). that seems logical
to me but we have many more knowledgable people here
who might be able to pick my suggestion apart. hope
it helps.

jeremy

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[Forrest]

hi danny,
here is part of what you may be looking for but i'm sure there is a
better way of describing the distance; hopefully someone knows a
better source.
it would depend on what order the solids are nested, but here is the
difference in the platonic solid duals: tetra to tetra, cube to
octahedron and icosahedron to dodecahedron.

inscribed to circumscribed sphere radius for tetrahedron to
tetrahedron = 33.33%

inscribed to circumscribed sphere radius ratio for both cube and
octahedron = 57.735%

inscribed to circumscribed sphere radius ratio for both icosahedron
and dodecahedron = 92.624%

from: http://blazelabs.com/f-p-solids.asp

best

neall

[Chris Hamilton]

> x = (2d * (n/7))+d, where n is the number of the solid
> (the octahedron would be three, tetrahedron four, cube
> five, etc.) jeremy

ok, so let me state this again for all of us who either had geometry a long
time ago or simply need to realize the shapes :) you are using 7 as a
denominator, but, i realistically only see 6 actual shapes : sphere,
icosohedron, octahedron, star tetrahedron, cube and dodecahedron. after
that, we go back to icosahedron and sphere. are you basing this #7 on
something else? this may prove how rusty i am in this stuff :) i won't ask
anything else, cuz all your work was based on the 7. i will wait til i see
your brilliant answer (as usual:) chris

[Chris Hamilton]

oh geez, just thought of something else...diameter is a relative figure in a
3d universe, right? if you have a circle, and everything is inside it (the 5
other shapes), then the diameter is the same for all shapes....right? chris

[RealiDan@...]

hi guys,

thanks for all of your replies. maybe i'm not understanding things
correctly, or maybe i'm just not wording it right. from what i have
gathered, as the sphere pulsates when energy strengthens and
weakens, the geometry inside them would need to change. i was
thinking that they "unfolded" in a set order like sphere, central
isoc,tetra,.......outer isoc, then sphere again representing the
octave of densities, sub-densities, sub-sub. etc, all the while
pulsating and changing the size of the sphere. maybe nested wasn't
the proper word to use, because as chris says the diameter would be
the same for all. the sides of those solids nested inside the same
sphere have the ratios listed in the table in "the shift of the
ages" chapter 13. i was just trying to think of a way to represent
the "spheres within spheres" or "circles within circles" on paper.
those phrases imply (express actually) spheres of different sizes.
so i thought maybe there were some set diameter ratios for the 8
different sized spheres beginning with the inner sphere (circle) out
to the outer sphere. so if we set the inner sphere to 1, then the
outer sphere (the octave) would be 2. the 6 spheres in between
would (or should, i think) have set ratios to the other spheres. i
wouldn't think that they would be spaced evenly between the inner
and outer sphere, especially since every other ratio having to do
with energy and growth has some version of phi or the square root of
2 etc. i'd better stop here, i'm talking in circles and my head is
spinning. :-)

danny



--- in asc2k@yahoogroups.com (/group/asc2k/post?postid=otq-nyo3-hhx-szywos4zo6xlsqkqilr1vtezop4lmg7vbac9ij-kcksthvcexdw2gvgthqcnfcze6eh), "chris hamilton"
<chris.hamilton2@v...> wrote:
> oh geez, just thought of something else...diameter is a relative
figure in a
> 3d universe, right? if you have a circle, and everything is inside
it (the 5
> other shapes), then the diameter is the same for all
shapes....right? chris

[Jeremy Weiland]

> you are using 7 as a denominator, but, i
> realistically only see 6 actual shapes : sphere,
> icosohedron, octahedron, star tetrahedron, cube and
> dodecahedron. after that, we go back to icosahedron
> and sphere. are you basing this #7 on something
> else?

there are seven positions in the octave before you
return to the first position - think of the musical
scale. see the first sphere as the base frequency of
the octave, and the last sphere will be the same
"note" but one octave up (or in other words the
frequency would be double that of the first).

the original question, as i understood it, was not
"which" shapes correspond to each position in the
octave, but rather how to calculate the relative
sizes. since the octave is just a doubling of
frequency that is divided into 7 distinct positions,
just divide up your diameter by 7 and add that to the
base diameter.

the frequency is the causal factor for light, sound,
and geometry. just because we have some repeating
shapes doesn't mean that, consequently, they represent
different frequency positions in the octave.

hope that helps.

love and light,

jeremy

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