posted on Jun, 15 2010 @ 01:32 PM
Before I even begin, I want to start off by apologizing for this very long post; feel free to scan through it quickly -- but I ask that you focus your
attention on my question concerning the missing 7th and 8th platonic "solids".
I am far from being any "Math Wiz", but perhaps that is because I'm more in tune with the "oneness", I tend to think that what we're being
taught by others isn't exactly the truth -
which ironically, makes a lot of sense... Anyway, I'd also like to thank you for doing your own personal research and taking the time to gather all
of this information for the rest of us. Because I don't quite understand all of the mathematical aspects of what you're communicating, I took the
time to do some of my own personal research.
As far as all of what you're saying goes, I'm very confused by the idea that there is an "octave of the platonic"; however, I'm not saying
you're wrong. This also makes a lot of sense to me. But out of this, I'm very confused by how all of this information is only showing the 5 platonic
solids (viewable by us in our 3rd dimensional consiousness) with a 6th platonic geometry supposably existing in the 4th dimension. To get to the
point, my question is what are the 7th and 8th platonic "solids"??? Any ideas????
For whatever reason, I feel that this is actually a very important point that is most likely being overlooked simply because we are "3rd dimensional
Anyway, here's some more information that I came across in trying to discover some more Patterns, so that I can better understand. To me it looks
like that we are focusing on convex polygons and overlooking the conclave polygons.
In trying to better understand and educate myself, it seems as though the concave polygons (7th and 8th platonic POLYTOPES [solid seems like a poor
choice of words]) are the CONVEX HULLS (see below information) "stringing" the octaves together, in infinity.. 8.
Are the missing 7th and 8th polytopes the 11-cell hendecachoron and the 57-cell? Ketchup???
Some more interesting info on Octal Systems (base 8 numerical sytems) rather than our normal 10 Base number system:
 By Native Americans
The Yuki language in California and the Pamean languages in Mexico have octal systems because the speakers count using the spaces between their
fingers rather than the fingers themselves.
 In Europe
In 1716 King Charles XII of Sweden asked Emanuel Swedenborg to elaborate a number system based on 64 instead of 10. Swedenborg however argued that for
people with less intelligence than the king such a big base would be too difficult and instead proposed 8 as base. In 1718 Swedenborg wrote a
manuscript, which has not been published: "En ny räknekonst som omväxlas vid talet 8 istället för det vanliga vid talet 10" ("A new arithmetic
(or art of counting) which changes at the Number 8 instead of the usual at the Number 10"). The numbers 1-7 are there denoted by the consonants l, s,
n, m, t, f, u (v) and zero by the vowel o. Thus 8 = "lo", 16 = "so", 24 = "no", 64 = "loo", 512 = "looo" etc. Numbers with consecutive
consonants are pronounced with vowel sounds between in accordance with a special rule.
 In fiction
* The fictional alien felinoid species Kilrathi of the Wing Commander universe count in octal, since their paws have four toes instead of 5.
* The Octospider species of Rama Revealed and the computer game RAMA use a colour code based on octal system, and its comprehension is a puzzle of
the game scenario.
* The Alterans from Stargate SG-1 use octal, even though they have ten fingers. It's possible that they count the gaps between each finger,
ignore the thumb on each hand, or use the thumb as a base-2 counter (as on an abacus) allowing them to count up to 30 (24 in decimal) on their
* The satirist Tom Lehrer famously remarked in his song parodying new math that "base 8 is just like base 10... if you're missing two
* In the first-person shooter Prey, numerical codes to open doors are entered in octal.
* The Tau race in the Warhammer 40,000 universe use the octal system.
* In The Beekeeper's Apprentice, Laurie R. King's first Sherlock Holmes pastiche featuring Mary Russell, base eight math played a key role in
solving the mystery.
* In the Star Wars universe, the alien race known as the Hutts counts in base eight, as they only have eight fingers.
* In the Niven/Pournelle novell Footfall the pachydermoid Fithp count in base eight and tend to group things into powers of eight, such as
military divisions of 64 soldiers. Niven's Kzin species also uses octal.
* The Na'vi from Avatar use octal, since they have four fingers on each hand.
 In computers
Octal is sometimes used in computing instead of hexadecimal, perhaps most often in modern times in conjunction with file permissions under Unix
systems (see chmod). It has the advantage of not requiring any extra symbols as digits (the hexadecimal system is base-16 and therefore needs six
additional symbols beyond 0–9). It is also used for digital displays.
At the time when octal originally became widely used in computing, systems such as the ICL 1900 and IBM mainframes employed 24-bit (or 36-bit) words.
Octal was an ideal abbreviation of binary for these machines because eight (or twelve) digits could concisely display an entire machine word (each
octal digit covering three binary digits). It also cut costs by allowing Nixie tubes, seven-segment displays, and calculators to be used for the
operator consoles, where binary displays were too complex to use, decimal displays needed complex hardware to convert radixes, and hexadecimal
displays needed to display more numerals.
All modern computing platforms, however, use 16-, 32-, or 64-bit words, further divided into eight-bit bytes. On such systems three octal digits per
byte would be required, with the most significant octal digit representing two binary digits (plus one bit of the next significant byte, if any).
Octal representation of a 16-bit word requires 6 digits, but the most significant octal digit represents (quite inelegantly) only one bit (0 or 1).
This representation offers no way to easily read the most significant byte, because it's smeared over four octal digits. Therefore, hexadecimal is
more commonly used in programming languages today, since two hexadecimal digits exactly specify one byte. Some platforms with a power-of-two word size
still have instruction subwords that are more easily understood if displayed in octal; this includes the PDP-11 and Motorola 68000 family. The
modern-day ubiquitous x86 architecture belongs to this category as well, but octal is rarely used on this platform.
In programming languages, octal literals are typically identified with a variety of prefixes, including the digit 0, the letters o or q, or the
digit–letter combination 0o. For example, the literal 73 (base 8) might be represented as 073, o73, q73, or 0o73 in various languages. Newer
languages have been abandoning the prefix 0, as decimal numbers are often represented with leading zeroes. The prefix q was introduced to avoid the
prefix o being mistaken for a zero, while the prefix 0o was introduced to avoid starting a numerical literal with an alphabetic character (like o or
q), since these might cause the literal to be confused with a variable name. The prefix 0o also follows the model set by the prefix 0x used for
hexadecimal literals in the C language.
Octal numbers that are used in some programming languages (C, Perl, PostScript…) for textual/graphical representations of byte strings when some
byte values (unrepresented in a code page, non-graphical, having special meaning in current context or otherwise undesired) have to be to escaped as
\nnn. Octal representation of non-ASCII bytes may be particularly handy with UTF-8, where any start byte has octal value \3nn and any continuation
byte has octal value \2nn.
The octave of the platonic goes from spere to icosa to the octahedron, then star tetrahedron (merkaba) then dodecahedron, icosa again then back to
sphere to round out the octave.
A convex polygon is a simple polygon whose interior is a convex set. The following properties of a simple polygon are all equivalent to
* Every internal angle is less than 180 degrees.
* Every line segment between two vertices remains inside or on the boundary of the polygon.
A simple polygon is strictly convex if every internal angle is strictly less than 180 degrees. Equivalently, a polygon is strictly convex if every
line segment between two nonadjacent vertices of the polygon is strictly interior to the polygon except at its endpoints.
--Every nondegenerate triangle is strictly convex. (from Wikipeida)
A polygon that is not convex is called concave or reentrant. A concave polygon will always have an interior angle with a measure that is
greater than 180 degrees.
It is possible to cut a concave polygon into a set of convex polygons. A polynomial-time algorithm for finding a decomposition into as few convex
polygons as possible is described by Chazelle & Dobkin (1985).
From Wikipedia, the free encyclopedia
In mathematics, the convex hull or convex envelope for a set of points X in a real vector space V is the minimal convex set containing X.
In computational geometry, a basic problem is finding the convex hull for a given finite nonempty set of points in the plane. It is common to use the
term "convex hull" for the boundary of that set, which is a convex polygon, except in the degenerate case that the points are collinear. The convex
hull is then typically represented by a sequence of the vertices of the line segments forming the boundary of the polygon, ordered along that