I believe this does it...

  #declare RhombicTriacontahedron =
  intersection
    {plane {-z, 1 rotate <58.28252558854,  -36, 0>}
     plane {-z, 1 rotate <58.28252558854, -108, 0>}
     plane {-z, 1 rotate <58.28252558854, -180, 0>}
     plane {-z, 1 rotate <58.28252558854, -252, 0>}
     plane {-z, 1 rotate <58.28252558854, -324, 0>}

     plane {z, 1 rotate <58.28252558854,  -36, 0>}
     plane {z, 1 rotate <58.28252558854, -108, 0>}
     plane {z, 1 rotate <58.28252558854, -180, 0>}
     plane {z, 1 rotate <58.28252558854, -252, 0>}
     plane {z, 1 rotate <58.28252558854, -324, 0>}

     plane {-y, 1 rotate <58.28252558854,  -36, 0>}
     plane {-y, 1 rotate <58.28252558854, -108, 0>}
     plane {-y, 1 rotate <58.28252558854, -180, 0>}
     plane {-y, 1 rotate <58.28252558854, -252, 0>}
     plane {-y, 1 rotate <58.28252558854, -324, 0>}

     plane {y, 1 rotate <58.28252558854,  -36, 0>}
     plane {y, 1 rotate <58.28252558854, -108, 0>}
     plane {y, 1 rotate <58.28252558854, -180, 0>}
     plane {y, 1 rotate <58.28252558854, -252, 0>}
     plane {y, 1 rotate <58.28252558854, -324, 0>}

     plane {-x, 1 rotate <58.28252558854,  -36, 0>}
     plane {-x, 1 rotate <58.28252558854, -108, 0>}
     plane {-x, 1 rotate <58.28252558854, -180, 0>}
     plane {-x, 1 rotate <58.28252558854, -252, 0>}
     plane {-x, 1 rotate <58.28252558854, -324, 0>}

     plane {x, 1 rotate <58.28252558854,  -36, 0>}
     plane {x, 1 rotate <58.28252558854, -108, 0>}
     plane {x, 1 rotate <58.28252558854, -180, 0>}
     plane {x, 1 rotate <58.28252558854, -252, 0>}
     plane {x, 1 rotate <58.28252558854, -324, 0>}
    }

Looks good to me... wasn't as complicated as I was expecting.

Carl

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