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

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 David Hartley Posts: 463 Registered: 12/13/04
Re: Deformable platonic "solids"
Posted: Feb 28, 2013 6:15 AM

In message <kgn0oe\$e31\$1@dont-email.me>, David Bernier
<david250@videotron.ca> writes
>Are all agreed that the dodecahedron is deformable?
>I'm myself not sure what to think at present.

My "squashing" process was completely wrong. It worked with half a
dodecahedron but cannot be made to work with both halves together.

However the twisting idea is definitely possible. You can twist one face
without moving any other vertices. The face just moves inwards. Note
that the adjacent faces are no longer faces, in the sense that they are
no longer planar polygons. I suspect that the dodecahedron can't be
deformed without that happening, unlike the cube.

Twisting a single face like that requires that each vertex only has one
edge connected to the rest of the frame, i.e. only three edges total at
each vertex. Only the cube and dodecahedron have that.
--
David Hartley