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 SchlĂ¤fli 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. george da champ!

2. 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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