// Hi Stephen,
//
// for texturing of the individual faces of a polyhedron you don't need
// any alignment, just give each plane of the intersection it's own pigment
// or texture and rotate it together with the plane. In the following
// declaration of a RhombicDodecahedron, replace the texture statements
// by your textures for the faces. For each of these textures, the area
// in the xy-plane with corners
//
//                sqrt(.5)*y
//    -x                              x
//               -sqrt(.5)*y
//
// is transferred to the face to which this texture belongs.
//
// I've added spheres in the corners; it's easy to calculate midpoints
// and face normals from their coordinates.
//
//    Sputnik
//
//
// ----------------------------

// fr### [at] computermuseumfh-kielde
// ----------------------------


// finish, textures =====================================================

#declare Fin = finish { ambient .4 diffuse .6 }

#declare Wood = texture {
  pigment { wood scale 0.05 rotate 87*y translate -0.3*z }
  finish { Fin }
  }

#declare Test = texture {
  pigment { image_map { png "test" } // test.png is in include directory
    translate <-0.5, -0.5, 0>
    scale <2, sqrt(2), 1>
    }
  finish { Fin }
  }


// declaration of rhombic dodecahedron ==================================

#declare RhombicDodecahedron =
  intersection {
    plane { -z, 0 texture { Wood } translate -z rotate <  0, 45, 45> }
    plane { -z, 0 texture { Test } translate -z rotate <  0, 45,-45> }
    plane { -z, 0 texture { Test } translate -z rotate <  0,-45, 45> }
    plane { -z, 0 texture { Test } translate -z rotate <  0,-45,-45> }

    plane { -z, 0 texture { Test } translate -z rotate <  0,225,-45> }
    plane { -z, 0 texture { Test } translate -z rotate <  0,225, 45> }
    plane { -z, 0 texture { Test } translate -z rotate <  0,135,-45> }
    plane { -z, 0 texture { Test } translate -z rotate <  0,135, 45> }

    plane { -z, 0 texture { Wood } translate -z rotate < 90,  0,  0> }
    plane { -z, 0 texture { Test } translate -z rotate < 90,  0, 90> }
    plane { -z, 0 texture { Test } translate -z rotate < 90,  0,180> }
    plane { -z, 0 texture { Test } translate -z rotate < 90,  0,-90> }

    bounded_by { sphere { 0, 1.42 } }

    }//intersection


// declaration of corners of rhombic dodecahedron =======================

#declare S = sqrt(.5);
#declare R = .05;
#declare Corners =
  union {
    union {
      sphere { < 0,  1,  S>, R }
      sphere { < 0,  1, -S>, R }
      sphere { < 0, -1,  S>, R }
      sphere { < 0, -1, -S>, R }
      sphere { < 1,  0,  S>, R }
      sphere { < 1,  0, -S>, R }
      sphere { <-1,  0,  S>, R }
      sphere { <-1,  0, -S>, R }
      texture { pigment { color blue 1 } finish { Fin } }
      }
    union {
      sphere { < 1,  1,  0>, R }
      sphere { < 1, -1,  0>, R }
      sphere { <-1,  1,  0>, R }
      sphere { <-1, -1,  0>, R }
      sphere { < 0,  0,  2*S>, R }
      sphere { < 0,  0, -2*S>, R }
      texture { pigment { color red 1 } finish { Fin } }
      }
    }


// calculate an midpoint, here normal vector = midpoint vector ==========

#declare Mid = ( <0, 1, -S> + <1, 0, -S> ) / 2; // =<0.5, 0.5, S>
// midpoints:  <+/- 0.5, +/- 0.5, +/- S>;  x;  -x;  y;  -y


// simple scene with textured rhombic dodecahedron etc. on plane ========

union {
  object { RhombicDodecahedron }
  object { Corners }
  cone { 0, 0.05, -0.8*z, 0
    texture { pigment { color green 1 } finish { Fin } }
    rotate <0, -45, 45> //or: transform { Reorient_Trans (-x, Mid) }
    translate Mid
    }
  scale 1 rotate 0*y translate <0, 0, 0>
  }

plane { y, -1-R
  texture {
    pigment { checker rgb <1, .9, .8>, rgb <.8, .7, .6> }
    finish { Fin }
    }
  }

light_source { <-1500, 2500, -2000>, color rgb 1 }

camera { location -10*z look_at 0 angle 20
  rotate <25, 20, 0> translate <0, 0, 0> }


// END ==================================================================

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