/* Platonic Solid Include File */
/* Written By S.R. Hall, of Ground-Net Graphics*/
/* version 1.0, December, 1998 */

/*
Contents:
I. Introduction
II.  How To Use This File
III.  Important Geometric Info On The Platonic Solids 
IV.  The Actual Object Listings
*/

/* 
I.  Introduction:
     This .inc file has solid and framework representations of the five 
   Platonic solids: 
   1) tetrahedron
   2) hexahedron {the cube} 
   3) octahedron
   4) dodecahedron
   5) icosahedron  
   All pieces ending with the "_e" suffix have edges of length one.
   Those that end with the "_r" suffix have radii (plural radius) of length one.
   The radius is defined in this case to be the distance from the geometric 
   center of the object to a vertex {or corner point}
   NOTE:  When any numeric value is given in this file, remember that they are
          ALL approximations (as is necessary to put into digital form), and may
          be slightly different from other sources, due to rounding at differing
          points in the calculations from the one used in the other sources.
*/    

/*
------------------------------------------------
II.  How To Use This File: 
1. if using a frame version, #declare the appropriate radius:
   for tetrahedrons --> tetra_radius
   for hexahedrons --> hexa_radius
   for octahedrons --> octa_radius
   for dodecahedrons --> dodeca_radius
   for icosahedrons --> icosa_radius
   This radius is for the thickness of the cylinders and spheres that
   make up the frame.
   The default radius for solids with edges of length one is .05.
   The default frame radius varies for solids with radius of length one,
   and is equal to the edge length of the solid times .05.
2. #declare "platonic.inc" (be sure platonic.inc is in your INCLUDE directory)
3. Then put 
     #declare object OBJECT_NAME=
      {
       xxxx_yyyy_z
       texture{...}
       rotate{...}
       ...(and whatever other object modifiers that pleases you) 
      }
    Notes: 1)OBJECT_NAME can be changed to whatever you want.
           2)xxxx is one of the following:
               a) tetra       
               b) hexa
               c) octa
               d) dodeca
               e) icosa
           3)yyyy is either:
               a) solid
               b) frame
           4)z is either:
               a) e {for edge length equals one}
               b) r {for radius length equals one}     
           5) an example of xxxx_yyyy_z:
              we want a framework version of a dodecahedron, where the edges
              are of length one----> we use dodeca_frane_e
           6) now use object in form --> object{OBJECT_NAME}
              however you want to use it.  (Remember, if you change OBJECT_NAME
              in the #declare, change it to the same thing in the object{}
              statement.
           7) the solids are all centered, geometrically, at <0,0,0>.  Thus,
              all vertices are the same distance from the POV origin, and the
              bottom halves of the solids would below a plane thus specified:
              plane{<0,1,0>,0 pigment{color White}}.  To get the solid to be
              resting on the plane (without rotations), translate the solid
              up an amount equal to the absolute value of height of the lowest
              point. To rest on any other object (without rotations), add the
              absolute value of height of the lowest point of the solid to the
              height of the top of the other object.  If you are using the frame
              version of the solids, add the radius of the frame into your
              calculations. 
       
------------------------------------------------
*/
    
/*
III.  Important Geometric Info On The Platonic Solids:  
   Tetrahedrons have four triangle sides, four vertices (plural vertex),
   and six edges.
   The radius of a tetrahedron with edge length of one is .6124.
   The edge length of a tetrahedron with radius equal to one is 1.6329.
   You don't have to tilt the tetrahedrons in this file to have them lay flat.
   The angle between sides is 70.5288 degrees.
   Assuming edge length of one:
   Highest point:  .6124
   Lowest point:  -.2041

   Hexahedrons, better known as cubes, in their solid forms, are more easily
   represented by the box statement in POV, but for consistency, are given in
   the mesh form.
   Hexahedrons have six square sides, eight vertices, and twelve edges.
   The radius of a hexahedron with edge length of one is .8660.
   The edge length of a hexahedron with radius equal to one is 1.1547.
   Hexahedrons in this file dont' have to be tilted to lay flat.
   The angle between sides is 90.0000 degrees.
   Assuming edge length of one:
   Highest point:  .5
   Lowest point:  -.5
   
   Octahedrons have eight triangle sides, six vertices, and twelve edges.
   The radius of an octahedron with edge length of one is .7071.
   The edge length of an octahedron with radius equal to one is 1.4142.
   Octahedrons have to be tilted (+/-)54.7356 degrees in the X or Z part of a
   rotation vector to lay flat (assuming no prior rotations of the octahedron).
   The height of the center of the octahedron above the "ground", when it is 
   laying flat is .4082, assuming edge length of one.  Remember, rotate around x,
   rotate around y (to whatever amount you want), then translate. 
   The angle between sides is 109.4712 degrees.  
   Assuming edge length of one:
   Highest point:  .7071 
   Lowest point:  -.7071 
                   
   Dodecahedrons have twelve pentagonal sides, twenty vertices, and thirty edges.
   The radius of a dodecahedron with edge length of one is 1.4014.
   The edge length of a dodecahedron with radius equal to one is .7136.
   Dodecahedrons in this file don't have to be tilted to lay flat.
   The angle between sides is 116.5651 degrees. 
   Highest point:  1.1137
   Lowest point:  -1.1137
   
   Icosahedrons have twenty triangle sides, twelve vertices, and thirty edges.
   The radius of an icosahedron with edge length of one is .9510.
   The edge length of an icosahedron with radius equal to one is 1.0515.
   Tilting icosahedrons to get them flat is a bit tricky. To get the icosahedron
   in this file to lay flat, the tilt angle is 37.3773, and the rotation must be
   done around the x axis (or simply rotate<37.3773,0,0>).  The height of the
   center of the icosahedron above the ground, when it is laying flat, is .7557,
   assuming an edge length of one.  Remember, rotate around x, rotate to whatever
   you want around y, then translate.
   The angle between sides is 138.1897 degrees.   
   Assuming edge length of one:
   Highest point:  .9510
   Lowest point:  -.9510

*/                  

/*
IV.  The Actual Object Listings
*/
   
#declare tetra_solid_e = mesh
{
 triangle{<-0.5000,-0.2041,-0.2887> < 0.5000,-0.2041,-0.2887> < 0.0000,-0.2041, 0.5774>}
 triangle{<-0.5000,-0.2041,-0.2887> < 0.5000,-0.2041,-0.2887> < 0.0000, 0.6124, 0.0000>}
 triangle{< 0.5000,-0.2041,-0.2887> < 0.0000,-0.2041, 0.5774> < 0.0000, 0.6124, 0.0000>}
 triangle{<-0.5000,-0.2041,-0.2887> < 0.0000,-0.2041, 0.5774> < 0.0000, 0.6124, 0.0000>}
}

#ifndef (tetra_radius)
#declare tetra_radius = 0.0500;
#end

#declare tetra_frame_e = union
{
 cylinder {<-0.5000,-0.2041,-0.2887> < 0.5000,-0.2041,-0.2887> tetra_radius open}
 cylinder {<-0.5000,-0.2041,-0.2887> < 0.0000,-0.2041, 0.5774> tetra_radius open}
 cylinder {< 0.5000,-0.2041,-0.2887> < 0.0000,-0.2041, 0.5774> tetra_radius open}
 cylinder {<-0.5000,-0.2041,-0.2887> < 0.0000, 0.6124, 0.0000> tetra_radius open}
 cylinder {< 0.5000,-0.2041,-0.2887> < 0.0000, 0.6124, 0.0000> tetra_radius open}
 cylinder {< 0.0000,-0.2041, 0.5774> < 0.0000, 0.6124, 0.0000> tetra_radius open}
 sphere {<-0.5000,-0.2041,-0.2887> tetra_radius}
 sphere {< 0.5000,-0.2041,-0.2887> tetra_radius}
 sphere {< 0.0000,-0.2041, 0.5774> tetra_radius}
 sphere {< 0.0000, 0.6124, 0.0000> tetra_radius}
}

#declare tetra_solid_r = object{tetra_solid_e scale 1.6329}

#declare tetra_frame_r = object{tetra_frame_e scale 1.6239}

#declare hexa_solid_e = mesh
{
 triangle{<-.5, .5,-.5> <-.5, .5, .5> <-.5,-.5, .5>}
 triangle{<-.5,-.5,-.5> <-.5,-.5, .5> <-.5, .5,-.5>}
 triangle{< .5, .5,-.5> < .5, .5, .5> < .5,-.5, .5>}
 triangle{< .5,-.5,-.5> < .5,-.5, .5> < .5, .5,-.5>}
 triangle{< .5, .5,-.5> < .5, .5, .5> <-.5, .5, .5>}
 triangle{<-.5, .5,-.5> <-.5, .5, .5> < .5, .5,-.5>}
 triangle{< .5,-.5,-.5> < .5,-.5, .5> <-.5,-.5, .5>}
 triangle{<-.5,-.5,-.5> <-.5,-.5, .5> < .5,-.5,-.5>}
 triangle{< .5,-.5, .5> < .5, .5, .5> <-.5, .5, .5>}
 triangle{<-.5,-.5, .5> <-.5, .5, .5> < .5,-.5, .5>}
 triangle{< .5,-.5,-.5> < .5, .5,-.5> <-.5, .5,-.5>}
 triangle{<-.5,-.5,-.5> <-.5, .5,-.5> < .5,-.5,-.5>}
}

#ifndef(hexa_radius)
#declare hexa_radius = 0.0500;
#end

#declare hexa_frame_e = union
{
 cylinder{< .5, .5, .5> < .5, .5,-.5> hexa_radius open}
 cylinder{<-.5, .5, .5> <-.5, .5,-.5> hexa_radius open}
 cylinder{< .5, .5, .5> <-.5, .5, .5> hexa_radius open}
 cylinder{< .5, .5,-.5> <-.5, .5,-.5> hexa_radius open}
 cylinder{< .5,-.5, .5> < .5,-.5,-.5> hexa_radius open}
 cylinder{<-.5,-.5, .5> <-.5,-.5,-.5> hexa_radius open}
 cylinder{< .5,-.5, .5> <-.5,-.5, .5> hexa_radius open}
 cylinder{< .5,-.5,-.5> <-.5,-.5,-.5> hexa_radius open}
 cylinder{< .5, .5, .5> < .5,-.5, .5> hexa_radius open}
 cylinder{< .5, .5,-.5> < .5,-.5,-.5> hexa_radius open}
 cylinder{<-.5, .5, .5> <-.5,-.5, .5> hexa_radius open}
 cylinder{<-.5, .5,-.5> <-.5,-.5,-.5> hexa_radius open}
 sphere{< .5, .5, .5> hexa_radius}    
 sphere{< .5, .5,-.5> hexa_radius} 
 sphere{< .5,-.5, .5> hexa_radius}    
 sphere{< .5,-.5,-.5> hexa_radius} 
 sphere{<-.5, .5, .5> hexa_radius}    
 sphere{<-.5, .5,-.5> hexa_radius} 
 sphere{<-.5,-.5, .5> hexa_radius}    
 sphere{<-.5,-.5,-.5> hexa_radius}  
}             

#declare hexa_solid_r = object{hexa_solid_e scale 1.1547}

#declare hexa_frame_r = object{hexa_frame_e scale 1.1547}

#declare octa_solid_e = mesh
{
 triangle{< .5, 0.0, .5>< .5, 0.0,-.5>< 0.0, .7071, 0.0>}    
 triangle{< .5, 0.0,-.5><-.5, 0.0,-.5>< 0.0, .7071, 0.0>}
 triangle{<-.5, 0.0,-.5><-.5, 0.0, .5>< 0.0, .7071, 0.0>}    
 triangle{<-.5, 0.0, .5>< .5, 0.0, .5>< 0.0, .7071, 0.0>}
 triangle{< .5, 0.0, .5>< .5, 0.0,-.5>< 0.0,-.7071, 0.0>}    
 triangle{< .5, 0.0,-.5><-.5, 0.0,-.5>< 0.0,-.7071, 0.0>}
 triangle{<-.5, 0.0,-.5><-.5, 0.0, .5>< 0.0,-.7071, 0.0>}    
 triangle{<-.5, 0.0, .5>< .5, 0.0, .5>< 0.0,-.7071, 0.0>}       
} 

#ifndef(octa_radius)
#declare octa_radius = 0.0500;
#end

#declare octa_frame_e = union
{
 cylinder{< .5, 0.0, .5>< 0.0, .7071, 0.0> octa_radius open}
 cylinder{< .5, 0.0,-.5>< 0.0, .7071, 0.0> octa_radius open}
 cylinder{<-.5, 0.0, .5>< 0.0, .7071, 0.0> octa_radius open}
 cylinder{<-.5, 0.0,-.5>< 0.0, .7071, 0.0> octa_radius open}
 cylinder{< .5, 0.0, .5>< 0.0,-.7071, 0.0> octa_radius open}
 cylinder{< .5, 0.0,-.5>< 0.0,-.7071, 0.0> octa_radius open}
 cylinder{<-.5, 0.0, .5>< 0.0,-.7071, 0.0> octa_radius open}
 cylinder{<-.5, 0.0,-.5>< 0.0,-.7071, 0.0> octa_radius open}      
 cylinder{< .5, 0.0, .5>< .5, 0.0,-.5> octa_radius open}
 cylinder{< .5, 0.0,-.5><-.5, 0.0,-.5> octa_radius open}       
 cylinder{<-.5, 0.0,-.5><-.5, 0.0, .5> octa_radius open}       
 cylinder{<-.5, 0.0, .5>< .5, 0.0, .5> octa_radius open}                               
 sphere{< .5, 0.0, .5> octa_radius}
 sphere{< .5, 0.0,-.5> octa_radius}
 sphere{<-.5, 0.0, .5> octa_radius}
 sphere{<-.5, 0.0,-.5> octa_radius}
 sphere{< 0.0, .7071, 0.0> octa_radius}
 sphere{< 0.0,-.7071, 0.0> octa_radius}     
}
                                
#declare octa_solid_r = object{octa_solid_e scale 1.4142}

#declare octa_frame_r = object{octa_frame_e scale 1.4142}

#declare dodeca_solid_e = mesh
{
//1 
 triangle{< 0, 1.1137, .8507>< .8090, 1.1137, .2629>< 0, 1.1137, 0>}
 triangle{< .8090, 1.1137, .2629>< .5, 1.1137, -.6882>< 0, 1.1137, 0>}
 triangle{< .5, 1.1137, -.6882>< -.5, 1.1137, -.6882>< 0, 1.1137, 0>}
 triangle{< -.5, 1.1137, -.6882>< -.8090, 1.1137, .2629>< 0, 1.1137, 0>}
 triangle{< -.8090, 1.1137, .2629>< 0, 1.1137, .8507>< 0, 1.1137, 0>}  
//2 
 triangle{< 0, 1.1137, .8507>< .8090, 1.1137, .2629>< .5852, 0.4981, .8055>}
 triangle{< 0, 1.1137, .8507>< 0, 0.2629, 1.3761>< .5852, 0.4981, .8055>}
 triangle{< .8090, 1.1137, .2629>< 1.3086, 0.2629, .4253>< .5852, 0.4981, .8055>}
 triangle{< 0, 0.2629, 1.3761>< .8088, -0.2629, 1.1132>< .5852, 0.4981, .8055>}
 triangle{< 1.3086, 0.2629, .4253>< .8088, -0.2629, 1.1132>< .5852, 0.4981, .8055>}
//3 
 triangle{< .8090, 1.1137, .2629>< .5, 1.1137, -.6882>< .9469, 0.4981, -.3077>}
 triangle{< .8090, 1.1137, .2629>< 1.3086, 0.2629, .4253>< .9469, 0.4981, -.3077>}
 triangle{< .5, 1.1137, -.6882>< .8088, 0.2629, -1.1132>< .9469, 0.4981, -.3077>}
 triangle{< 1.3086, 0.2629, .4253>< 1.3086, -0.2629, -.4253>< .9469, 0.4981, -.3077>}
 triangle{< .8088, 0.2629, -1.1132>< 1.3083, -0.2629, -.4253>< .9469, 0.4981, -.3077>}
//4 
 triangle{< .5, 1.1137, -.6882>< -.5, 1.1137, -.6882>< 0, 0.4981, -.9958>}
 triangle{< .5, 1.1137, -.6882>< .8088, 0.2629, -1.1132>< 0, 0.4981, -.9958>}
 triangle{< -.5, 1.1137, -.6882>< -.8088, 0.2629, -1.1132>< 0, 0.4981, -.9958>}
 triangle{< .8088, 0.2629, -1.1132>< 0, -0.2629, -1.3761>< 0, 0.4981, -.9958>}
 triangle{< -.8088, 0.2629, -1.1132>< 0, -0.2629, -1.3761>< 0, 0.4981, -.9958>}  
//5
 triangle{< -.5, 1.1137, -.6882>< -.8090, 1.1137, .2629>< -.9469, 0.4981, -.3077>}
 triangle{< -.5, 1.1137, -.6882>< -.8088, 0.2629, -1.1132>< -.9469, 0.4981, -.3077>}
 triangle{< -.8090, 1.1137, .2629>< -1.3086, 0.2629, .4253>< -.9469, 0.4981, -.3077>}
 triangle{< -.8088, 0.2629, -1.1132>< -1.3086, -0.2629, -.4253>< -.9469, 0.4981, -.3077>}
 triangle{< -1.3086, 0.2629, .4253>< -1.3086, -0.2629, -.4253>< -.9469, 0.4981, -.3077>}
//6
 triangle{< -.8090, 1.1137, .2629>< 0, 1.1137, .8507>< -.5852, 0.4981, .8055>}
 triangle{< -.8090, 1.1137, .2629>< -1.3086, 0.2629, .4253>< -.5852, 0.4981, .8055>}
 triangle{< 0, 1.1137, .8507>< 0, 0.2629, 1.3761>< -.5852, 0.4981, .8055>}
 triangle{< -1.3086, 0.2629, .4253>< -.8088, -0.2629, 1.1132>< -.5852, 0.4981, .8055>}
 triangle{< 0, 0.2629, 1.3761>< -.8088, -0.2629, 1.1132>< -.5852, 0.4981, .8055>}
//7 
 triangle{< 0,-1.1137, -.8507>< -.8090,-1.1137, -.2629>< 0,-1.1137, 0>}
 triangle{< -.8090,-1.1137, -.2629>< -.5,-1.1137, .6882>< 0,-1.1137, 0>}
 triangle{< -.5,-1.1137, .6882>< .5,-1.1137, .6882>< 0,-1.1137, 0>}
 triangle{< .5,-1.1137, .6882>< .8090,-1.1137, -.2629>< 0,-1.1137, 0>}
 triangle{< .8090,-1.1137, -.2629>< 0,-1.1137, -.8507>< 0,-1.1137, 0>}
//8 
 triangle{< 0, -1.1137, -.8507>< -.8090, -1.1137, -.2629>< -.5852, -0.4981, -.8055>}
 triangle{< 0, -1.1137, -.8507>< 0, -0.2629, -1.3761>< -.5852, -0.4981, -.8055>}
 triangle{< -.8090, -1.1137, -.2629>< -1.3086, -0.2629, -.4253>< -.5852, -0.4981, -.8055>}
 triangle{< 0, -0.2629, -1.3761>< -.8088, 0.2629, -1.1132>< -.5852, -0.4981, -.8055>}
 triangle{< -1.3086, -0.2629, -.4253>< -.8088, 0.2629, -1.1132>< -.5852, -0.4981, -.8055>}
//9 
 triangle{< -.8090, -1.1137, -.2629>< -.5, -1.1137, .6882>< -.9469, -0.4981, .3077>}
 triangle{< -.8090, -1.1137, -.2629><-1.3086, -0.2629,-.4253>< -.9469, -0.4981, .3077>}
 triangle{< -.5, -1.1137, .6882><-.8088, -0.2629, 1.1132>< -.9469, -0.4981, .3077>}
 triangle{< -1.3086, -0.2629, -.4253><-1.3086, 0.2629, .4253>< -.9469, -0.4981, .3077>}
 triangle{< -.8088, -0.2629, 1.1132><-1.3086, 0.2629, .4253>< -.9469, -0.4981, .3077>}
//10
 triangle{< -.5, -1.1137, .6882>< .5, -1.1137, .6882>< 0, -0.4981, .9958>}
 triangle{< -.5, -1.1137, .6882><-.8088, -0.2629, 1.1132>< 0, -0.4981, .9958>}
 triangle{< .5, -1.1137, .6882><.8088, -0.2629, 1.1132>< 0, -0.4981, .9958>}
 triangle{<-.8088, -0.2629,1.1132><0, 0.2629,1.3761>< 0, -0.4981, .9958>}
 triangle{<.8088, -0.2629,1.1132><0, 0.2629,1.3761>< 0, -0.4981, .9958>}
//11
 triangle{< .5, -1.1137, .6882>< .8090, -1.1137, -.2629>< .9469, -0.4981, .3077>}
 triangle{< .5, -1.1137, .6882><.8088, -0.2629,1.1132>< .9469, -0.4981, .3077>}
 triangle{< .8090, -1.1137, -.2629><1.3086, -0.2629,-.4253>< .9469, -0.4981, .3077>}
 triangle{<.8088, -0.2629,1.1132><1.3086, 0.2629,.4253>< .9469, -0.4981, .3077>}
 triangle{<1.3086, -0.2629,-.4253><1.3086, 0.2629,.4253>< .9469, -0.4981, .3077>}
//12 
 triangle{< .8090, -1.1137, -.2629>< 0, -1.1137, -.8507>< .5852, -0.4981, -.8055>}
 triangle{< .8090, -1.1137, -.2629><1.3086, -0.2629,-.4253>< .5852, -0.4981, -.8055>}
 triangle{< 0, -1.1137, -.8507><0, -0.2629,-1.3761>< .5852, -0.4981, -.8055>}
 triangle{<1.3086, -0.2629,-.4253><.8088, 0.2629,-1.1132>< .5852, -0.4981, -.8055>}
 triangle{<0, -0.2629,-1.3761><.8088, 0.2629,-1.1132>< .5852, -0.4981, -.8055>} 
}                                

#ifndef(dodeca_radius)
#declare dodeca_radius = 0.0500;
#end

#declare dodeca_frame_e = union
{
 cylinder{ < 0 , 1.1137, .8507> < .8090 , 1.1137, .2629> dodeca_radius open}
 cylinder{ < .8090 , 1.1137, .2629> < .5 , 1.1137, -.6882> dodeca_radius open}  
 cylinder{ < .5 , 1.1137, -.6882> < -.5, 1.1137, -.6882> dodeca_radius open}
 cylinder{ < -.5, 1.1137, -.6882> < -.8090, 1.1137, .2629> dodeca_radius open}
 cylinder{ < -.8090, 1.1137, .2629> < 0 , 1.1137, .8507> dodeca_radius open}
 cylinder{ < 0 , 1.1137, .8507> < 0 , .2629, 1.3761> dodeca_radius open}
 cylinder{ < .8090 , 1.1137, .2629> < 1.3086 , .2629, .4253> dodeca_radius open}  
 cylinder{ < .5 , 1.1137, -.6882> < .8088, .2629, -1.1132> dodeca_radius open}
 cylinder{ < -.5, 1.1137, -.6882> < -.8088, .2629, -1.1132> dodeca_radius open}
 cylinder{ < -.8090, 1.1137, .2629> < -1.3086, .2629, .4253> dodeca_radius open}
 cylinder{ < .8088, -.2629, 1.1132> < 0 , .2629, 1.3761> dodeca_radius open}
 cylinder{ < 1.3086, -.2629, -.4253> < 1.3086 , .2629, .4253> dodeca_radius open}  
 cylinder{ < 0 , -.2629, -1.3761> < .8088, .2629, -1.1132> dodeca_radius open}
 cylinder{ < -1.3086, -.2629, -.4253> < -.8088, .2629, -1.1132> dodeca_radius open}
 cylinder{ < -.8088, -.2629, 1.1132> < -1.3086, .2629, .4253> dodeca_radius open}
 cylinder{ < -.8088, -.2629, 1.1132> < 0 , .2629, 1.3761> dodeca_radius open}
 cylinder{ < .8088, -.2629, 1.1132> < 1.3086 , .2629, .4253> dodeca_radius open}  
 cylinder{ < 1.3086, -.2629, -.4253>  < .8088, .2629, -1.1132> dodeca_radius open}
 cylinder{ < 0 , -.2629, -1.3761> < -.8088, .2629, -1.1132> dodeca_radius open}  
 cylinder{ < -1.3086, -.2629, -.4253> < -1.3086, .2629, .4253> dodeca_radius open} 
 cylinder{ < 0 , -1.1137, -.8507> < 0, -.2629, -1.3761> dodeca_radius open}
 cylinder{ < -.8090, -1.1137, -.2629> < -1.3086, -.2629, -.4253> dodeca_radius open}
 cylinder{ < -.5, -1.1137, .6882> < -.8088, -.2629, 1.1132> dodeca_radius open}  
 cylinder{ < .5, -1.1137, .6882>< .8088, -.2629, 1.1132> dodeca_radius open}
 cylinder{ < .8090, -1.1137, -.2629> < 1.3086, -.2629, -.4253> dodeca_radius open}
 cylinder{ < 0 , -1.1137, -.8507> < .8090 , -1.1137, -.2629> dodeca_radius open}
 cylinder{ < .8090 , -1.1137, -.2629> < .5 , -1.1137, .6882> dodeca_radius open}
 cylinder{ < .5 , -1.1137, .6882> < -.5, -1.1137, .6882> dodeca_radius open}  
 cylinder{ < -.5, -1.1137, .6882> < -.8090, -1.1137, -.2629> dodeca_radius open}
 cylinder{ < -.8090, -1.1137, -.2629> < 0 , -1.1137, -.8507> dodeca_radius open}                                              
 sphere{< 0 , 1.1137, .8507> dodeca_radius} 
 sphere{< .8090 , 1.1137, .2629> dodeca_radius}
 sphere{< .5 , 1.1137, -.6882> dodeca_radius}
 sphere{< -.5, 1.1137, -.6882> dodeca_radius}
 sphere{< -.8090, 1.1137, .2629> dodeca_radius}
 sphere{< 0 , .2629, 1.3761> dodeca_radius} 
 sphere{< 1.3086 , .2629, .4253> dodeca_radius}
 sphere{< .8088, .2629, -1.1132> dodeca_radius}
 sphere{< -.8088, .2629, -1.1132> dodeca_radius}
 sphere{< -1.3086, .2629, .4253> dodeca_radius}
 sphere{< 0, -.2629, -1.3761> dodeca_radius} 
 sphere{< -1.3086, -.2629, -.4253> dodeca_radius}
 sphere{< -.8088, -.2629, 1.1132> dodeca_radius}
 sphere{< .8088, -.2629, 1.1132> dodeca_radius}
 sphere{< 1.3086, -.2629, -.4253> dodeca_radius}
 sphere{< 0 , -1.1137, -.8507> dodeca_radius} 
 sphere{< -.8090 , -1.1137, -.2629> dodeca_radius}
 sphere{< -.5 , -1.1137, .6882> dodeca_radius}
 sphere{< .5 , -1.1137, .6882> dodeca_radius}
 sphere{< .8090, -1.1137, -.2629> dodeca_radius}                                              
}

#declare dodeca_solid_r = object{dodeca_solid_e scale .7316}

#declare dodeca_frame_r = object{dodeca_frame_e scale .7316}

#declare icosa_solid_e = mesh
{
//1
 triangle{<0,.9510,0><0,.4253,.8507><.8090,.4253,.2629>}
 triangle{<0,.9510,0><.8090,.4253,.2629><.5,.4253,-.6882>}
 triangle{<0,.9510,0><.5,.4253,-.6882><-.5,.4253,-.6882>}
 triangle{<0,.9510,0><-.5,.4253,-.6882><-.8090,.4253,.2629>}
 triangle{<0,.9510,0><-.8090,.4253,.2629><0,.4253,.8507>}
//2
 triangle{<.5,-.4253,.6882><0,.4253,.8507><.8090,.4253,.2629>}
 triangle{<.8090,-.4253,-.2629><.8090,.4253,.2629><.5,.4253,-.6882>}
 triangle{<0,-.4253,-.8507><.5,.4253,-.6882><-.5,.4253,-.6882>}
 triangle{<-.8090,-.4253,-.2629><-.5,.4253,-.6882><-.8090,.4253,.2629>}
 triangle{<-.5,-.4253,.6882><-.8090,.4253,.2629><0,.4253,.8507>}  
//3
 triangle{<.5,.4253,-.6882><0,-.4253,-.8507><.8090,-.4253,-.2629>}
 triangle{<.8090,.4253,.2629><.8090,-.4253,-.2629><.5,-.4253,.6882>}
 triangle{<0,.4253,.8507><.5,-.4253,.6882><-.5,-.4253,.6882>}
 triangle{<-.8090,.4253,.2629><-.5,-.4253,.6882><-.8090,-.4253,-.2629>}
 triangle{<-.5,.4253,-.6882><-.8090,-.4253,-.2629><0,-.4253,-.8507>}  
//4
 triangle{<0,-.9510,0><0,-.4253,-.8507><.8090,-.4253,-.2629>}
 triangle{<0,-.9510,0><.8090,-.4253,-.2629><.5,-.4253,.6882>}
 triangle{<0,-.9510,0><.5,-.4253,.6882><-.5,-.4253,.6882>}
 triangle{<0,-.9510,0><-.5,-.4253,.6882><-.8090,-.4253,-.2629>}
 triangle{<0,-.9510,0><-.8090,-.4253,-.2629><0,-.4253,-.8507>}          
} 

#ifndef(icosa_radius)
#declare icosa_radius = 0.0500;
#end

#declare icosa_frame_e = union
{
 cylinder{<0,.9510,0> <0,.4253,.8507> icosa_radius open} 
 cylinder{<0,.9510,0> <.8090,.4253,.2629> icosa_radius open}
 cylinder{<0,.9510,0> <.5,.4253,-.6882> icosa_radius open}
 cylinder{<0,.9510,0> <-.5,.4253,-.6882> icosa_radius open}
 cylinder{<0,.9510,0> <-.8090,.4253,.2629> icosa_radius open}
 cylinder{<0,.4253,.8507> <.8090,.4253,.2629> icosa_radius open} 
 cylinder{<.8090,.4253,.2629> <.5,.4253,-.6882> icosa_radius open}
 cylinder{<.5,.4253,-.6882> <-.5,.4253,-.6882> icosa_radius open}
 cylinder{<-.5,.4253,-.6882> <-.8090,.4253,.2629> icosa_radius open}
 cylinder{<-.8090,.4253,.2629> <0,.4253,.8507> icosa_radius open}
 cylinder{<.5,-.4253,.6882> <0,.4253,.8507> icosa_radius open} 
 cylinder{<.8090,-.4253,-.2629> <.8090,.4253,.2629> icosa_radius open}
 cylinder{<0,-.4253,-.8507> <.5,.4253,-.6882> icosa_radius open}
 cylinder{<-.8090,-.4253,-.2629> <-.5,.4253,-.6882> icosa_radius open}
 cylinder{<-.5,-.4253,.6882> <-.8090,.4253,.2629> icosa_radius open}
 cylinder{<-.5,-.4253,.6882> <0,.4253,.8507> icosa_radius open} 
 cylinder{<.5,-.4253,.6882> <.8090,.4253,.2629> icosa_radius open}
 cylinder{<.8090,-.4253,-.2629> <.5,.4253,-.6882> icosa_radius open}
 cylinder{<0,-.4253,-.8507> <-.5,.4253,-.6882> icosa_radius open}
 cylinder{<-.8090,-.4253,-.2629> <-.8090,.4253,.2629> icosa_radius open}
 cylinder{ <0,-.4253,-.8507> <-.8090,-.4253,-.2629> icosa_radius open} 
 cylinder{ <-.8090,-.4253,-.2629> <-.5,-.4253,.6882> icosa_radius open}
 cylinder{ <-.5,-.4253,.6882> <.5,-.4253,.6882> icosa_radius open}
 cylinder{ <.5,-.4253,.6882> <.8090,-.4253,-.2629> icosa_radius open}
 cylinder{ <.8090,-.4253,-.2629> <0,-.4253,-.8507> icosa_radius open}
 cylinder{<0,-.9510,0> <0,-.4253,-.8507> icosa_radius open} 
 cylinder{<0,-.9510,0> <-.8090,-.4253,-.2629> icosa_radius open}
 cylinder{<0,-.9510,0> <-.5,-.4253,.6882> icosa_radius open}
 cylinder{<0,-.9510,0> <.5,-.4253,.6882> icosa_radius open}
 cylinder{<0,-.9510,0> <.8090,-.4253,-.2629> icosa_radius open}                  
 sphere{<0,.9510,0> icosa_radius}
 sphere{<0,.4253,.8507> icosa_radius}
 sphere{<.8090,.4253,.2629> icosa_radius}
 sphere{<.5,.4253,-.6882> icosa_radius}
 sphere{<-.5,.4253,-.6882> icosa_radius}
 sphere{<-.8090,.4253,.2629> icosa_radius}
 sphere{<0,-.4253,-.8507> icosa_radius}
 sphere{<-.8090,-.4253,-.2629> icosa_radius}
 sphere{<-.5,-.4253,.6882> icosa_radius}
 sphere{<.5,-.4253,.6882> icosa_radius}
 sphere{<.8090,-.4253,-.2629> icosa_radius}
 sphere{<0,-.9510,0> icosa_radius}                       
}

#declare icosa_solid_r = object{icosa_solid_e scale 1.0515}

#declare icosa_frame_r = object{icosa_frame_e scale 1.0515}