//tetrahedron, cube, octahedron, dodecahedron and icosahedron
//center<->vertex radius is always 1 unit

#declare p = array[4]
{<0,1,0>,
 <0,-.333333,.942809>,
 <.816497,-.333333,-.471405>,
 <-.816497,-.333333,-.471405>}
#declare Tetrahedron = mesh {
   triangle { p[0],p[1],p[2] }
   triangle { p[0],p[1],p[3] }
   triangle { p[0],p[2],p[3] }
   triangle { p[1],p[2],p[3] }
}

#declare Cube = mesh {
   triangle { <-1,-1,-1>,<-1,-1,1>,<-1,1,1> }
   triangle { <-1,-1,-1>,<-1,1,-1>,<-1,1,1> }
   triangle { <-1,-1,-1>,<-1,-1,1>,<1,-1,1> }
   triangle { <-1,-1,-1>,<1,-1,-1>,<1,-1,1> }
   triangle { <-1,-1,-1>,<-1,1,-1>,<1,1,-1> }
   triangle { <-1,-1,-1>,<1,-1,-1>,<1,1,-1> }
   triangle { <1,1,1>,<1,1,-1>,<1,-1,-1> }
   triangle { <1,1,1>,<1,-1,1>,<1,-1,-1> }
   triangle { <1,1,1>,<1,1,-1>,<-1,1,-1> }
   triangle { <1,1,1>,<-1,1,1>,<-1,1,-1> }
   triangle { <1,1,1>,<-1,1,1>,<-1,-1,1> }
   triangle { <1,1,1>,<1,-1,1>,<-1,-1,1> }
   scale 0.57735026919
}

#declare Octahedron = mesh {
   triangle { <0,1,0>,<0,0,1>,<1,0,0> }
   triangle { <0,1,0>,<1,0,0>,<0,0,-1> }
   triangle { <0,1,0>,<0,0,-1>,<-1,0,0> }
   triangle { <0,1,0>,<-1,0,0>,<0,0,1> }
   triangle { <0,-1,0>,<0,0,1>,<1,0,0> }
   triangle { <0,-1,0>,<1,0,0>,<0,0,-1> }
   triangle { <0,-1,0>,<0,0,-1>,<-1,0,0> }
   triangle { <0,-1,0>,<-1,0,0>,<0,0,1> }
}

#declare p = array[20]
{< 0.642889,-0.884861, 0.208887>,
 < 0.000000, 0.884861,-0.675973>,
 < 0.642889, 0.884861,-0.208887>,
 < 0.397327, 0.884861, 0.546874>,
 <-0.397327, 0.884861, 0.546874>,
 <-0.642889, 0.884861,-0.208887>,
 < 0.000000, 0.208887,-1.093748>,
 < 1.040216, 0.208887,-0.337987>,
 < 0.642889, 0.208887, 0.884861>,
 <-0.642889, 0.208887, 0.884861>,
 <-1.040216, 0.208887,-0.337987>,
 < 0.000000,-0.208887, 1.093748>,
 <-1.040216,-0.208887, 0.337987>,
 <-0.642889,-0.208887,-0.884861>,
 < 0.642889,-0.208887,-0.884861>,
 < 1.040216,-0.208887, 0.337987>,
 < 0.000000,-0.884861, 0.675973>,
 <-0.642889,-0.884861, 0.208887>,
 <-0.397327,-0.884861,-0.546874>,
 < 0.397327,-0.884861,-0.546874>}
#declare Dodecahedron = mesh {
   triangle { p[01],p[02],p[03] } triangle { p[01],p[03],p[04] } triangle { p[01],p[04],p[05] }
   triangle { p[01],p[02],p[07] } triangle { p[01],p[07],p[14] } triangle { p[01],p[14],p[06] }
   triangle { p[02],p[03],p[08] } triangle { p[02],p[08],p[15] } triangle { p[02],p[15],p[07] }
   triangle { p[03],p[04],p[09] } triangle { p[03],p[09],p[11] } triangle { p[03],p[11],p[08] }
   triangle { p[04],p[05],p[10] } triangle { p[04],p[10],p[12] } triangle { p[04],p[12],p[09] }
   triangle { p[05],p[01],p[06] } triangle { p[05],p[06],p[13] } triangle { p[05],p[13],p[10] }
   triangle { p[18],p[19],p[14] } triangle { p[18],p[14],p[06] } triangle { p[18],p[06],p[13] }
   triangle { p[19],p[00],p[15] } triangle { p[19],p[15],p[07] } triangle { p[19],p[07],p[14] }
   triangle { p[00],p[16],p[11] } triangle { p[00],p[11],p[08] } triangle { p[00],p[08],p[15] }
   triangle { p[16],p[17],p[12] } triangle { p[16],p[12],p[09] } triangle { p[16],p[09],p[11] }
   triangle { p[17],p[18],p[13] } triangle { p[17],p[13],p[10] } triangle { p[17],p[10],p[12] }
   triangle { p[16],p[17],p[18] } triangle { p[16],p[18],p[19] } triangle { p[16],p[19],p[00] }
   scale .898056
}

#declare p = array[12]
{<0,1,0>,
 < 0.000000, 0.447213, 0.894427>,
 < 0.850651, 0.447213, 0.276393>,
 < 0.525731, 0.447213,-0.723607>,
 <-0.525731, 0.447213,-0.723607>,
 <-0.850651, 0.447213, 0.276393>,
 <-0.000000,-0.447213,-0.894427>,
 <-0.850651,-0.447213,-0.276393>,
 <-0.525731,-0.447213, 0.723607>,
 < 0.525731,-0.447213, 0.723607>,
 < 0.850651,-0.447213,-0.276393>,
 <0,-1,0> }
#declare Icosahedron = mesh {
   triangle { p[00],p[01],p[02] } triangle { p[00],p[02],p[03] }
   triangle { p[00],p[03],p[04] } triangle { p[00],p[04],p[05] }
   triangle { p[00],p[05],p[01] } triangle { p[01],p[02],p[09] }
   triangle { p[02],p[03],p[10] } triangle { p[03],p[04],p[06] }
   triangle { p[04],p[05],p[07] } triangle { p[05],p[01],p[08] }
   triangle { p[01],p[08],p[09] } triangle { p[09],p[10],p[02] }
   triangle { p[10],p[06],p[03] } triangle { p[06],p[07],p[04] }
   triangle { p[07],p[08],p[05] } triangle { p[11],p[06],p[07] }
   triangle { p[11],p[07],p[08] } triangle { p[11],p[08],p[09] }
   triangle { p[11],p[09],p[10] } triangle { p[11],p[10],p[06] }
}

#undef p