Platonic solids in a forest of spheres

Overlapping spheres make fertile ground.

The basis of Sacred Geometry comes down to the simply elegant, single sphere. Put your protractor point on any point of its circumference and describe another sphere. For more about the importance of spheres in morphology, check out my post on geodesics.

Two more spheres arise from those intersecting arcs; and so on, and so on. What you end up with is a very habit-forming experience, so if you’re an obsessive grapho-maniac then proceed with caution – it is addictive! I drew all the images in this post with a very cheap plastic protractor, highlighter pens and markers, ink pen, and white correcting fluid.


flower of life

pencil and marker on paper with highlighter
___________________

 

 fruit of life
pencil and marker on paper with highlighter
__________________

 

 Arise, Platonic solids

The Platonic solids are iconic elements of form that can be derived from the line segments that triangulate the spheres of the fruit of life, as you can see in Metatron’s cube above. To draw Metatron’s cube, all you have to do is connect the centres of each sphere to all the other spheres, resulting in 72 lines.

 

 Metatron’s cube
pencil and marker on paper with highlighter
___________________

The 5 Platonic solids: Tetrahedron, Cube or (Hexahedron), Octahedron, Dodecahedron and Icosahedron are primal models of crystal patterns found in countless variations throughout the world of minerals. As such, they are a central player in the Biotensegrity conversation because certain iterations of these ideal shapes underpin the molecular structure of proteins as well as the crystalline fascial matrices that network to form the largest and most innervated sensory organ of our bodies.

Although we refer to them eponymously as “Platonic,” these shapes actually proliferated in ancient cultures all over the world. For example, in Scotland as sandstone sculpture dating as far back as 2000BC, now at the Ashmolean Museum at Oxford:

These archetypal polyhedra have a special place at the table of Sacred Geometry due to their elemental quality. Many cultures associated the elements with 3D forms and as such their perception of all matter in the Universe was based on the five polyhedra, including human anatomy.

This context gave rise to Humoural Theory, which was in practice centuries before Plato and Hippocrates, and used in cultures throughout Persia, India, and China. The tridosha theory of prakrti in Ayurveda is a well known example dear to many yoga practitioners. The humours are still an influential basis of traditional materia medica around the world, and are intimately related to the elements and what we now refer to in the West as the Platonic solids.

Plato described his eponymous forms around 300BC and attributed to them the qualities of nature:

  • tetrahedron: fire
  • octahedron: air
  • cube: earth
  • icosahedron: water
  • dodecahedron: ether, or Universe

The Platonic solids are also called the regular solids or regular polyhedra. They are convex, with equivalent faces composed of congruent convex regular polygons, and as such all their faces are identical. Their angles are always less than 360 degrees, as each of them could be carved out of a sphere. This is important in relation to geodesics.

 

 Tetrahedron
pencil and marker on paper with highlighter and whiteout (tipex)

__________

 

 Octahedron
pencil and marker on paper with highlighter and whiteout
__________

 Cube
pencil and marker on paper with highlighter and whiteout
__________


 Dodecahedron
pencil and marker on paper with highlighter and whiteout
__________

 Icosahedron
pencil and marker on paper with highlighter and whiteout

I have found that, like everything else worth knowing, to really get the Platonic solids is to draw them yourself from the spheres. Not just once, but over and over, like repeating a mantra until it flows out of you. Once you have spent some time following their forms and feeling their faces, it gets easier to see how they stack up in nature.

 Links and thanks:

http://www.pbs.org/wgbh/nova/blogs/physics/2011/12/beautiful-losers-platos-geometry-of-elements/

http://www.mathematicsmagazine.com/Articles/SacredGeometryPlatonicSolids.php#.WB2nIpN97GI

http://mathworld.wolfram.com/PlatonicSolid.html

2 Replies to “Platonic solids in a forest of spheres”

Leave a Reply

Your email address will not be published. Required fields are marked *