//EXAMPLE OF PROJECTION OF 24 Cell

//Files with predefined colors and textures
#include "colors.inc"
#include "glass.inc"
#include "golds.inc"
#include "metals.inc"
#include "stones.inc"
#include "woods.inc"

//Place the camera
camera {
   sky <0,0,1>          //Don't change this
   direction <-1,0,0>   //Don't change this
   right <-4/3,0,0>     //Don't change this
   location  <10,20,30>  //Camera location
   look_at   <0,0,0>    //Where camera is pointing
   angle 10       //Angle of the view
}

//Ambient light to "brighten up" darker pictures
global_settings { ambient_light White }
global_settings { max_trace_level 10 }


//Place a light
light_source {
   <10,20,30>
   color White*2
}

//Set a background color
background { color White }

//List the vertices of the 24 Cell
#declare p =
  array[24][4]
  {
   { 0, 0,-1,-1}, //0
   { 0, 0,-1, 1}, //1
   { 0, 0, 1,-1}, //2
   { 0, 0, 1, 1}, //3
   { 0,-1, 0,-1}, //4
   { 0,-1, 0, 1}, //5
   { 0, 1, 0,-1}, //6
   { 0, 1, 0, 1}, //7
   { 0,-1,-1, 0}, //8
   { 0,-1, 1, 0}, //9
   { 0, 1,-1, 0}, //10
   { 0, 1, 1, 0}, //11
   {-1, 0, 0,-1}, //12
   {-1, 0, 0, 1}, //13
   { 1, 0, 0,-1}, //14
   { 1, 0, 0, 1}, //15
   {-1, 0,-1, 0}, //16   
   {-1, 0, 1, 0}, //17
   { 1, 0,-1, 0}, //18
   { 1, 0, 1, 0}, //19
   {-1,-1, 0, 0}, //20
   {-1, 1, 0, 0}, //21
   { 1,-1, 0, 0}, //22
   { 1, 1, 0, 0}  //23
  };

//Create the array to collect the projected points
#declare q = array[24];

//Specify the direction of projection
#declare a=1;
#declare b=1;
#declare c=1;
#declare d=1;

//Project the points
#declare l=sqrt(a*a+b*b+c*c+d*d);
#declare i=0;
#while(i<24)
  #declare q[i]=
    < (d*p[i][0]+c*p[i][1]-b*p[i][2]-a*p[i][3])/l,
      (-c*p[i][0]+d*p[i][1]+a*p[i][2]-b*p[i][3])/l,
      (b*p[i][0]-a*p[i][1]+d*p[i][2]-c*p[i][3])/l >;
  #declare i=i+1;
#end


#declare r=.035;

//96 Edges of the projection
union{

cylinder {q[0],  q[4],r}   
cylinder {q[0],  q[6],r}
cylinder {q[0],  q[8],r}
cylinder {q[0],  q[10],r} 
cylinder {q[0],  q[12], r}
cylinder {q[0],  q[14], r}
cylinder {q[0],  q[16], r}  
cylinder {q[0],  q[18], r}  
cylinder {q[1],  q[5], r}
cylinder {q[1],  q[7], r}
cylinder {q[1],  q[8], r}  
cylinder {q[1],  q[10], r} 
cylinder {q[1],  q[13], r}
cylinder {q[1],  q[15], r}
cylinder {q[1],  q[16], r}  
cylinder {q[1],  q[18], r}  
cylinder {q[2],  q[4], r}
cylinder {q[2],  q[6], r}
cylinder {q[2],  q[9], r}
cylinder {q[2],  q[11], r} 
cylinder {q[2],  q[12], r}
cylinder {q[2],  q[14], r}
cylinder {q[2],  q[11], r}  
cylinder {q[2],  q[17], r}  
cylinder {q[2],  q[19], r}  
cylinder {q[3],  q[5], r}
cylinder {q[3],  q[7], r}
cylinder {q[3],  q[9], r}  
cylinder {q[3],  q[11], r} 
cylinder {q[3],  q[13], r}
cylinder {q[3],  q[15], r}
cylinder {q[3],  q[17], r}  
cylinder {q[3],  q[19], r}   
cylinder {q[4],  q[8], r}
cylinder {q[4],  q[9], r}
cylinder {q[4],  q[12], r}
cylinder {q[4],  q[14], r}  
cylinder {q[4],  q[20], r}   
cylinder {q[4],  q[22], r} 
cylinder {q[5],  q[8], r}
cylinder {q[5],  q[9], r}
cylinder {q[5],  q[13], r}
cylinder {q[5],  q[15], r}  
cylinder {q[5],  q[20], r}  
cylinder {q[5],  q[22], r} 
cylinder {q[6],  q[10], r} 
cylinder {q[6],  q[11], r}
cylinder {q[6],  q[12], r}
cylinder {q[6],  q[14], r}  
cylinder {q[6],  q[21], r}   
cylinder {q[6],  q[23], r} 
cylinder {q[7],  q[10], r}
cylinder {q[7],  q[11], r}
cylinder {q[7],  q[13], r}
cylinder {q[7],  q[15], r}  
cylinder {q[7],  q[21], r}   
cylinder {q[7],  q[23], r} 
cylinder {q[8],  q[16], r}
cylinder {q[8],  q[18], r}  
cylinder {q[8],  q[20], r}   
cylinder {q[8],  q[22], r}
cylinder {q[9],  q[17], r}
cylinder {q[9],  q[19], r}
cylinder {q[9],  q[20], r}
cylinder {q[9],  q[22], r}
cylinder {q[10], q[16], r}
cylinder {q[10], q[18], r}
cylinder {q[10], q[21], r}
cylinder {q[10], q[23], r} 
cylinder {q[11], q[17], r}
cylinder {q[11], q[19], r}
cylinder {q[11], q[21], r}
cylinder {q[11], q[23], r}   
cylinder {q[12], q[6], r} 
cylinder {q[12], q[16], r}
cylinder {q[12], q[17], r}
cylinder {q[12], q[20], r}  
cylinder {q[12], q[21], r}
cylinder {q[13], q[16], r}
cylinder {q[13], q[17], r}
cylinder {q[13], q[20], r}  
cylinder {q[13], q[21], r}
cylinder {q[14], q[18], r}
cylinder {q[14], q[19], r}
cylinder {q[14], q[22], r}  
cylinder {q[14], q[23], r}
cylinder {q[15], q[18], r}
cylinder {q[15], q[19], r}
cylinder {q[15], q[22], r}  
cylinder {q[15], q[23], r} 
cylinder {q[16], q[20], r}
cylinder {q[16], q[21], r} 
cylinder {q[17], q[20], r}
cylinder {q[17], q[21], r} 
cylinder {q[18], q[22], r} 
cylinder {q[18], q[23], r}    
cylinder {q[19], q[22], r}
cylinder {q[19], q[23], r}


texture {T_Gold_1A}
}

//Vertices of the projection
union{
sphere{q[0],r}
sphere{q[1],r}
sphere{q[2],r}
sphere{q[3],r}
sphere{q[4],r}
sphere{q[5],r}
sphere{q[6],r}
sphere{q[7],r}
sphere{q[8],r}
sphere{q[9],r}
sphere{q[10],r}
sphere{q[11],r}
sphere{q[12],r}
sphere{q[13],r}
sphere{q[14],r}
sphere{q[15],r}
sphere{q[16],r}
sphere{q[17],r}
sphere{q[18],r}
sphere{q[19],r}
sphere{q[20],r}
sphere{q[21],r}
sphere{q[22],r}
sphere{q[23],r}
texture {T_Gold_1A}
}