#include "shapes.inc"
#include "colors.inc"
#include "textures.inc"

background{color Gray60}

//The picture is showing (the real points of a part of) the 
//Barth-sextic, an algebraic
//surface in complex three-dimensional projective space with
// 65 double points, given by
//the equation:

//4(t^2 x^2 - y^2)(t^2 y^2 - z^2)(t^2 z^2 - x^2) -
// (1+2t)(x^2 + y^2 + z^2 - 1)^2 = 0
//  t = 0.5*(1 + sqrt(5))



//sextic
poly { 6<
0, 0, 0, 0, -27.41640786499874, 0, 0, 
  10.47213595499958, 0, -4.23606797749979, 0, 0, 0, 
  0, 0, 0, 0, 0, 0, 0, 10.47213595499958, 0, 0, 
  67.77708763999664, 0, -8.47213595499958, 0, 0, 0, 
  0, -27.41640786499874, 0, -8.47213595499958, 0, 
  8.47213595499958, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
  -27.41640786499874, 0, -4.23606797749979, 0, 0, 0, 
  0, 10.47213595499958, 0, -8.47213595499958, 0, 
  8.47213595499958, 0, 0, 0, 0, 0, 0, 0, 0, 
  -4.23606797749979, 0, 8.47213595499958, 0, 
  -4.23606797749979>




   scale < 30,30,30>
   texture {
      pigment {Red }
      finish {
	 phong 1.0
	 phong_size 10
	 ambient 0.4
	 diffuse 0.4
         reflection 0.2    
      }

   }
clipped_by{sphere{<0,0,0>40}}
rotate<0,0,0>
}
/*
// Put down  
plane {
   y, -20.0
   texture {
      pigment {
          color Gray40 
         
      }
      finish {
	 ambient 0.0
	 diffuse 0.4
      }
   }

}
*/
camera {
   location  <50.2, 20.3, -70.5>
   up        <0.0, 1.0,  0.0>
   right     <4/3, 0.0,  0.0>
   look_at   <0.1, 0.1,  0.1>
}

light_source { <200,500,-100> White
    spotlight
    radius  100
    falloff 200
    point_at <0,0,0>
}


//light_source { <1000, 300, -1301> color White }

light_source { <-101, -41, -131> color White }