Tesseract central projection

// https://commons.wikimedia.org/wiki/File:Tesseract_Schlegel_numbered.png
// height/width=20/19, e.g. +H4000 +W3800

#version 3.6;
global_settings { assumed_gamma 1.0 }
#default{ finish{ ambient 0.1 diffuse 0.9 conserve_energy}}

#include "colors.inc"


////////////////////////////////////////////////////////////////////////

#declare Camera_Position = <4, 7, -30>;
camera{
    location Camera_Position
    right    x*image_width/image_height
    angle    11
    look_at  <-.15, -.2, 0>
}


light_source{ <-400, 500, -300> color White*0.9 shadowless}
light_source{ <400, 200, 100> color White*0.4 shadowless}
light_source{ Camera_Position  color rgb<0.9,0.9,1>*0.2 shadowless}
sky_sphere{ pigment{ White } }


////////////////////////////////////////////////////////////////////////

#declare RadEdge = .01;
#declare RadVert = .05;
#declare RadScale = .6;

#declare VertexRankParities = array[16]{ 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0 }

#declare Scale = .47;
#declare P = array[16]{
    <-1,-1,-1>, <-1,1,-1>, <-1,-1,1>, <-1,1,1>, <1,-1,-1>, <1,1,-1>, <1,-1,1>, <1,1,1>,
    <-1,-1,-1>*Scale, <-1,1,-1>*Scale, <-1,-1,1>*Scale, <-1,1,1>*Scale, <1,-1,-1>*Scale, <1,1,-1>*Scale, <1,-1,1>*Scale, <1,1,1>*Scale
};

#declare Edges = array[32]{ array[2]{0, 1}, array[2]{0, 2}, array[2]{1, 3}, array[2]{2, 3}, array[2]{0, 4}, array[2]{1, 5}, array[2]{4, 5}, array[2]{2, 6}, array[2]{4, 6}, array[2]{3, 7}, array[2]{5, 7}, array[2]{6, 7}, array[2]{0, 8}, array[2]{1, 9}, array[2]{8, 9}, array[2]{2, 10}, array[2]{8, 10}, array[2]{3, 11}, array[2]{9, 11}, array[2]{10, 11}, array[2]{4, 12}, array[2]{8, 12}, array[2]{5, 13}, array[2]{9, 13}, array[2]{12, 13}, array[2]{6, 14}, array[2]{10, 14}, array[2]{12, 14}, array[2]{7, 15}, array[2]{11, 15}, array[2]{13, 15}, array[2]{14, 15} };

#declare Faces = array[24]{ array[4]{0, 1, 2, 3}, array[4]{0, 1, 4, 5}, array[4]{0, 2, 4, 6}, array[4]{1, 3, 5, 7}, array[4]{2, 3, 6, 7}, array[4]{4, 5, 6, 7}, array[4]{0, 1, 8, 9}, array[4]{0, 2, 8, 10}, array[4]{1, 3, 9, 11}, array[4]{2, 3, 10, 11}, array[4]{8, 9, 10, 11}, array[4]{0, 4, 8, 12}, array[4]{1, 5, 9, 13}, array[4]{4, 5, 12, 13}, array[4]{8, 9, 12, 13}, array[4]{2, 6, 10, 14}, array[4]{4, 6, 12, 14}, array[4]{8, 10, 12, 14}, array[4]{3, 7, 11, 15}, array[4]{5, 7, 13, 15}, array[4]{9, 11, 13, 15}, array[4]{6, 7, 14, 15}, array[4]{10, 11, 14, 15}, array[4]{12, 13, 14, 15} };


////////////////////////////////////////////////////////////////////////

union{

    // VERTICES
    union{
        #for( Index, 0, 15 )
            #if(Index<8)   #local R = RadVert;   #else   #local R = RadVert*RadScale;   #end
            sphere{
                P[Index], R
                #if(VertexRankParities[Index])
                    pigment{color rgb<1,0.8,0.65>*.2}
                #else
                    pigment{color rgb<1,0.8,0.65>*.5}
                #end
            }
        #end
    }

    // EDGES
    union{
        #for( Index, 0, 31 )
            #local EdgeArray = Edges[Index];
            #local A = EdgeArray[0];
            #local B = EdgeArray[1];
            #if(A<8)   #local RadA = RadEdge;   #else   #local RadA = RadEdge*RadScale;   #end
            #if(B<8)   #local RadB = RadEdge;   #else   #local RadB = RadEdge*RadScale;   #end
            cone{ P[A], RadA, P[B], RadB }
        #end
        pigment{color rgb .5}
    }

    // FACES
    union{
        #for( Index, 0, 23 )
            #local FaceArray = Faces[Index];
            polygon{ 5, P[FaceArray[0]], P[FaceArray[1]], P[FaceArray[3]], P[FaceArray[2]], P[FaceArray[0]] }
        #end
        pigment{color rgbt<0, 0, 1, .8>}
    }

    // VERTEX LABELS
    #for( Index, 0, 15 )
        text { ttf "/usr/share/fonts/truetype/msttcorefonts/Arial.ttf",  str(Index,2,0),  .03,  0

            #if(Index<8)   scale .11   #else   scale .085   #end    // labels for the inner cube are smaller

            translate P[Index]   // move label from center to vertex

            #if(Index<8)  // OUTSIDE

                #if(mod(div(Index,4),2))  // RIGHT
                    translate .1*x
                #else                     // LEFT
                    translate -.1*x
                #end

                #if(mod(Index, 2))  // TOP
                    translate .068*y
                #else               // BOTTOM
                    translate -.068*y
                #end

                translate <-.063, -.035, 0>

            #else         // INSIDE

                #if(mod(div(Index,4),2))  // RIGHT
                    translate -.08*x
                #else                     // LEFT
                    translate .08*x
                #end

                #if(mod(Index, 2))  // TOP
                    translate -.062*y
                #else               // BOTTOM
                    translate .062*y
                #end

                translate <-.05, -.032, 0>

            #end

        }
    #end

    scale 2.25

}