"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

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