The simplest way to make an octahedron is the intersection of two
rectangular boxes.

object {intersection {
  object {box{<-2,-1,-1>, <2,1,1>} rotate 45*x}
  object {box{<-1,-1,-2>, <1,1,2>} rotate 45*z}
  pigment {color Green}
  finish {roughness .1 specular .1} }
}

    Note that since the diagonal aspect is sqrt(2) you can take the 2's
above to 1.414 or so with the same results.  If you make it smaller than
that, it will trim the equator very nicely.  Now, two more rectangular
solids can trim the remaining 8 edges with no trouble at all.  Two solids,
one octahedron.  Four solids, one trimmed octahedron.
    For a perfectly symmetrical octahedron, scale the z axis to 1.414, for
obvious reasons.

Cheers!

Chip Shults
My robotics, space and CGI web page - http://home.cfl.rr.com/aichip

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