Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

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

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Frederick Williams

Posts: 2,164
Registered: 10/4/10
Re: Deformable platonic "solids"
Posted: Feb 27, 2013 4:02 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Ken Pledger wrote:
> 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.

Hmm... Suppose, instead of regular polyhedra we consider others some of
the faces of which may be quadrilaterals which have no edges parallel.
Such polyhedra may be deformable. So it seems to me that some property
other than having parallel edges adjacent to a face is relevant. But
thank you for considering the matter.

I can imagine twisting a dodecahedron so that of two parallel faces one
remains fixed while the other is turned about the axis that runs through
the center of them both. If I was good with my hands I'd make a model.

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 Diverting

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.