Saturday, November 25, 2017

The 25 Interrelations of the Platonic Solids

Once upon a time, back in the first years of the 1970s, I saw a page in Keith Critchlow's Order in Space that showed all 25 interrelations of the Platonic 5 Solids (tetrahedron, hexahedron or cube, octahedron, pentagonal dodecahedron, and icosahedron) and how they fit inside each other.  Over the years, I built all 25. 



I've also made magnetic models of some of these structures but not all of them and the nets are not all perfect but I did my best.  A couple of times I've tried to send these nets to Critchlow but they were returned unopened.  Oh well.

As with the Quanta Set that make up the Platonic Solids (http://geometrylinks.blogspot.com/2017/11/4-symmetrical-tetrahedra-of-5-platonic.html), I'd like see these built as class 2 tensegrities with spherical magnets at the vertices.




It would also be interesting to build them on the same scale at the Quanta Set.

The following are the nets of the 28 different polyhedra that comprise the 25 Interrelations of the Platonic Solids.


TetraSet

 HexaSet.1


















HexaSet.2





















OctaSet





















DodecaSet





















IcosaSet.1


IcosaSet.2










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