"Dave Matthews" <dma### [at] wrmnwestmnscuedu> wrote in message
news:web.42139c1c7cff8ff58c7259570@news.povray.org...
> "James Buddenhagen" <jbu### [at] REMOVEtexasnet> wrote:
> > Interesting pictures, but I'm not sure I see the same vertices.  In any case
the
> > vertices of 'my' three triangles were vertices of the cubeoctahedron,
namely:
> >
> > triangle 1:  <-1, 1, 0>, <0, -1, 1>, <1, 0, -1>
> > triangle 2:  <-1, -1, 0>, <0, 1, -1>, <1, 0, 1>
> > triangle 3:  <-1, 0, 1>, <0, -1, -1>, <1, 1, 0>
> > triangle 4:  <0, 1, 1>, <1, -1, 0>, <-1, 0, -1>
> >
> > I put a crude wireframe animation of the morphing of cubeoctahedron to
snubcube
> > temporarily here:
http://www.buddenbooks.com/jb/misc/cubeoct_snubcube_anim.gif
> > (306k)
> >
> > Jim Buddenhagen
>
> The gold balls on my pictures (the vertices of the yellow wireframe shapes)
> form the vertices of your cubeoctahedron.  The 4 at the top correspond to
> the 4 vertices at the top of your 4 intersecting triangles, etc.  In fact,
> the yellow frames in my pictures look identical to the start of your .gif
>
> To see my "morphing" in reverse, take your initial gif cubeoctahedron, look
> at the square faces, rotate each of them by 45 degrees and collapse them
> in, until they fit snug -- you get a cube.  Now take the triangular faces,
> rotate them each by 60 degrees and collapse them in -- you get an
> octahedron.
>
> Anyway, I noticed the cubeoctahedron shape of the vertices of your triangle,
> and recognized the resulting shape of my outward twists of cube and
> octahedron (which would make sense.)
>
> Your morphing .gif is interesting, also.  Thanks.
>
> Dave Matthews

Here is a pic that shows how 'my' triangles fit into a cubeoctahedron.
The 4 vertices at the top, as you say, are the top vertices of
the 4 triangles.

Jim Buddenhagen

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