Thursday, November 16, 2017

4 Symmetrical Tetrahedra of 5 Platonic Solids

This is a video of a magnetic model of the Cube and the Tetrahedron broken down into its smallest symmetrical tetrahedra, what Buckminster Fuller called the A and B Quanta or mathematicians call Schläfli orthoschemes (I think).

The A and B Quanta make the equilateral triangle Tetrahedron (4 sided solid), square Cube or Hexahedron (6 sided), and equilateral triangle Octahedron (8 sided)

The A Quanta is 1/24th of a Tetrahedron, the smallest symmetrical tetrahedron to make up a Platonic solid.  Here is the net of the A Quanta which can be folded to make the left and right hand versions, both of which are needed.

The B Quanta plus the A Quanta makes the Cube or Hexahedron 
and the Octahedron,
two other Platonic solids
48 A Quanta + 24 B Quanta = 1 Cube
2 Cubes = 1 Octahedron



A third, the Dodeca Quanta, builds the Dodecahedron

120 Dodeca Quanta = 1 Dodecahedron

And a fourth,
120 Icosa Quanta = 1 Icosahedron  

I've made magnetic models of the 5 Platonic solids with the magnets in the centers of the faces of the polyhedra.  The A and B Quanta have the same volumes and I suspect share that volume at the same scale, all four tetrahedra share one common right angle triangle, but I haven't tested that hypothesis.

Since I saw this video, I think the next model should be a set of these Quanta built as class 2 tensegrities with ball magnets at the vertices.  In fact, I'd commission someone to build it, for the right price.


  1. Thanks for using my clip of the class 2 tensegrity tetrahedron :) I admire the cube made of quanta, as it playfully demonstrates how the Platonic Solids relate to each other. I haven't experimented much with asymmetric tensegrities, nor with magnets. Looking forward to explore these areas.

    1. Thanks for reaching out.

      I tried to reach you a few years ago about commissioning the models I'm thinking of. Do you want to give me an estimate of costs?

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