The Secret of the Platypus

PLATONIC SOLID POETRY (an explanation)

To celebrate the common consciousness (and Mother Nature’s dear old templates), I have constructed poetry sets built on mathematics derived from the Platonic Solids. These shapes are at the root of many natural phenomena and were also considered by the ancient Greeks to represent ascending levels of consciousness. The poems are presented in sets of five, each representing the essence of a different platonic solid. When the poems are presented, the syllable structure is notated in parenthesis next to the poem name. The 5 poems (shapes) can appear in any order, and often the sequence is suggested thematically by Plato’s elemental interpretations of the shapes. The formula for each syllable structure is “shape edge length” over “radius of shape’s circumscribing sphere”. After much study I felt this was the best way to convey the different mathematical ‘personality’ of the shapes.

Most often, the first poem of each set of five is built on the ratios inherent in the TETRAHEDRON (4-sided pyramid).  The ratio of this shape’s edge to the radius of its circumscribing sphere is √6/4, or .612 which I found could be simplified with the ratio 30/49.  Put 30 syllables in the first stanza (6 lines of 5 syllables), and 49 syllables in the second stanza (7 lines of 7 syllables).  See? I told you it was simple.  Ma Nature uses the tetrahedron’s economy of strength to create such obscure compounds as H­2O.  Yep.  Water is a tetrahedral form.  So are the amino acids in the human body.  I figure “good enough for amino acids, good enough for poetry.” By creating these poems, keep in mind you are also re-enacting the same ratios that have been at work in nature since the beginning of American Idol and probably even earlier. Plato associated this shape with the element of FIRE.

The second poem of each set of five is built on the HEXAHEDRON (cube), whose shape edge to radius is √3/2, or .866 which can also be expressed as 13/15. This is a quickie. 13 syllables in the first stanza (broken into three lines of 5 syl, 3 syl, then 5 syl) then 15 syllables in the second stanza (3 lines with 5 syls each).  Sodium Chloride (NaCl) is a cubic structure.  So is the poem you can make here. Cool, huh?  Plato associated this very strong and boxy structure with the element of EARTH.


Ok, we’re onto the third now.  This is a big fave of mine: the 8 sided shape called the OCTAHEDRON. The personality ratio of the octahedron is √2/2, or .707 which can be approximated as 29/41.  It’s a cool one, because the stanzas break into syllables in a staggering way.  First stanza is 29 syllables over 5 lines (5,7,5,7,5).  Second stanza is 41 syllables over 7 lines (5,7,5,7,5,7,5).  Isn’t it striking that all these shapes’ ratios can be expressed in 5s and 7s?  There are abundant examples of this shape in nature- especially in crystal form, but I’m a big fan of the way it appears in mythologies… the four corners of the earth (the square of the cross-section) and the points of heaven atop and underworld below.  Plato’s association for the octahedron? Air.

This is a cool one.  Must be if Plato associated the shape with The Universe as a whole. The DODECAHEDRON was considered to be the embodiment of all the other solids, as well as a damn fine capsule for interdimensional travel for Ellie Arroway in the movie Contact.   It’s a twelve sided-figure, so it’s easy to compare it to our systems of time, as well.  Oh. The poem.  The ratio of shape edge to radius of its circumscribing sphere is 1/4(√15+√3), or 1.401 which I express as 7/5. So the first stanza is 7 syllables and the second stanza is 5 syllables.  Knock yourself out, bucketholders!


Last but not least is the ICOSAHEDRON. 20 sides.  Plato equated this shape with the element of water.  The personality ratio for this one is 1/4 √10+2√5, or .951 which can be expressed as 20/21. So the first stanza has 20 syllables (4 lines of 5 syllables). Second stanza has 21 syllables (3 lines of 7 syllables).  This shape realizes itself frequently in nature as the herpes viruses, and Dungeons & Dragons dice. Coincidence? You decide.

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