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Dodecahedral Shape-shifter

 
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robertw
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Joined: 10 Jan 2008
Posts: 395
Location: Melbourne, Australia

PostPosted: Sat Apr 04, 2009 1:35 pm    Post subject: Dodecahedral Shape-shifter Reply with quote

Hey,

I just uploaded photos of a new shape I made. This one is flexible! It can transform between a regular dodecahedron and a rhombic dodecahedron.


http://www.software3d.com/DodMorph.php

There's even a YouTube video of it in action Smile

Rob.
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oxenholme



Joined: 16 Jan 2008
Posts: 83
Location: North West England

PostPosted: Wed May 13, 2009 7:29 am    Post subject: Reply with quote

I'm lousy at mathematics, but does this imply that the volume of a regular dodecahedron is twice the cube of tau (1.6180339etc) times its edge length?
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robertw
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Joined: 10 Jan 2008
Posts: 395
Location: Melbourne, Australia

PostPosted: Wed May 13, 2009 9:30 am    Post subject: Reply with quote

No, because when in rhombic dodecahedral form, there are some gaps inside (although the orange parts do fold flat against each other).

However it is true of the rhombic dodecahedron, that it has twice the volume of a cube whose edge is the length of one of the rhombus's short diagonals.

Rob.
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