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

background{color Gray60}

/*
 This surface can be transformed into Steiner's Roman Surface or
 Cross-Cap Surface by a complex projective change of coordinates,
 but not by a real transformation.  It has two pinch points and
 three double lines, and, unlike the Roman or Cross-Cap, is not compact
 in any affine neighborhood.affine implicit:x^2*y^2-x^2*z^2+y^2*z^2-x*y*z=0
*/

//Steiner relative
poly { 4<
   0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 
   0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
 >
   scale < 20,20,20>
   texture {
      pigment {Plum }
      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>
}

camera {
   location  <30.2, 35.3, -70.5>
   up        <0.0, 1.0,  0.0>
   right     <4/3, 0.0,  0.0>
   look_at   <0.1, -6.1,  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 }