The Archimedean Solids & Their Dual Catalan Solids

The Archimedean solids and their duals the Catalan solids are less well known than the Platonic solids.  Whereas the Platonic solids are composed of one shape, these forms that Archimedes wrote about are made of at least two different shapes, all forming identical vertices.  They are 13 polyhedra of this type.  And since each solid has a ‘dual’ there are also 13 Catalan solids.  There are 26 in total.  If  our two-dimensional letters of the alpha-bet were three dimensional forms, these solids would be a great representation of our language. Subscribe to Blog via Email Enter your email address to subscribe to this blog…

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The Dodecad

Dodecahedron Flower of Life

The numbers 1 through 12 are what’s called the Dodecad.  Do means 2.  Decad means 10. These are not just numbers, but qualities of reality and the numerical armature that nature uses to build herself.  There’s twelve hours on the clock, twelve inches in a foot, and twelve signs of the Zodiac.  Have these measures any correlation? Is it all just a big coincidence? “There are too many coincidences for it to be all just coincidence” – unknown This is 99.99% accurate according to NASA in 2014.  Now, NASA has been known to lie… Perhaps they are just playing a trick…

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Cosmic Proportions

Earth Moon and Phi

The physical sizes of Earth and Moon are encoded into the proportions and measurements we commonly use in our daily lives.  From Renaissance artists to 21st century school teachers, we all use these cosmic proportions.  Very few are cognizant of their underlying meaning. If our Moon sat directly tangent to Earth, these are the proportions that arise.  The circumference of the circle is equal to the perimeter of the square to 99.97% accuracy according to NASA’s own data. The Great Pyramid’s dimensions can be broken down to 7 high, and 11 across.  The perimeter of the base equals the circumference of…

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The Platonic and Pythagorean Solids

Platonic Elements

The Platonic solids are 3-dimensional forms that nature uses to build herself.  The mental construct of reality seen in the form of geometry.     There are only five of them, naturally, since it is this (phi)veness that generates life as we know it. The Platonic, Pythagorean, or Perfect Solids: Let’s imagine you are on the inside of a sphere and are asked to make a bunch of different three-dimensional forms using only straight lines that all touch the surface of the sphere.  You could make all kinds, an infinite amount actually.  But if every line had to be of equal length, and…

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5040 The Perfect Number

Plato mentions in his Laws that 5040 is a convenient number to use for dividing many things (including both the citizens and the land of a state) into lesser parts.  Claiming it to be the ideal population of a city, he thought that the people’s well-being depended almost as much on the number as on justice.  5040 as it turns out is a very special number. One of the reasons 5040 was so highly revered was because it is a superior highly composite number.  Translation: No other number below it has as many divisors.  5040 has the same amount of divisors as…

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