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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Deformable platonic "solids"
Replies: 23   Last Post: Mar 12, 2013 8:11 PM

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Ken.Pledger@vuw.ac.nz

Posts: 1,275
Registered: 12/3/04
Re: Deformable platonic "solids"
Posted: Feb 27, 2013 3:33 PM
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In article <512E5CBC.9738E289@btinternet.com>,
Frederick Williams <freddywilliams@btinternet.com> wrote:

> Suppose the platonic solids aren't solid at all but are made of rigid
> line segments with completely flexible hinges at the vertices. The cube
> can be flattened into a... um... non cube. The tetrahedron, octahedron
> and icosahedron cannot be deformed at all. But what about the
> dodecahedron, can it be deformed?


Here's an intuitive line of thought, not a complete proof.

Starting from a face of the cube, the four adjacent edges are
parallel. That seems to be what permits the deformation. None of the
other regular polyhedra has parallel edges adjacent to a face, so I
suspect none can be deformed.

Ken Pledger.

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