```Date: Feb 28, 2013 1:27 AM
Author: dan.ms.chaos@gmail.com
Subject: Re: Deformable platonic "solids"

On Feb 27, 9:21 pm, Frederick Williams <freddywilli...@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?> --> When a true genius appears in the world, you may know him by> this sign, that the dunces are all in confederacy against him.> Jonathan Swift: Thoughts on Various Subjects, Moral and DivertingThe question can be formalized in the following manner :Define a 'semi-Platonic' solid as a solid with equal number of edgesper face , same number of faces as a regular counterpart , all edgesof the same length .It's the same as a Platonic solid , just drop the condition of equalangles per face , and the 'planar' nature of faces  .The question is : Is a 'semi-Platonic' solid necessarily platonic?That means , for a Platonic solid , does there exist a solid with thesame properties except different angles?As pointed  out , solids with triangular faces are not deformable .(being an equilateral triangle uniquely determines angles , as opposedto having a higher number of sides)As calculated , all Platonic solids with non-triangular faces aredeformable .
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