"Dave Matthews" <n@nn.n> wrote in message news:4212d2f4@news.povray.org...
> James Buddenhagen wrote:
> > While morphing between a snubcube and a cuboctahedron
> > I spotted a nice arrangement of diagonals forming these
> > interlocking triangles.
> >
> > Jim Buddenhagen
> That is very nice!  I was playing around with the same shapes (cube and
> octahedron), a while ago, but never noticed the diagonal vertices.  What
> I did notice, was that rotating the faces of the cube 45 degrees and
> out, gives the same shape as rotating the faces of the octahedron 60
> degrees and out -- and the vertices are identically those of your
> interlocking triangles (what is it, a snubcube or a cuboctahedron?)  But
> the triangles -- that's really fascinating.
>
> Dave Matthews

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

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