Enjoy!
Richard Schorn

// Persistence of Vision Ray Tracer Scene Description File
// File: polystar.pov
// Vers: 3.1
// Desc: great stellated dodecahedron
// Date: November 2000
// Auth: Richard Schorn (Ric### [at] t-onlinede)


// The computation of the coordinates was accomplished with
// the program DERIVE.

// You may need to adjust some lines due to word wrapping.

#version 3.1

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

global_settings
{
  assumed_gamma 1.0
}

// start for random number generation
#declare start = 19320501;
#declare s=seed(start);

// constant values
#declare re = 4 // radius of "edges"
#declare turn = <22,57,81> // argument for rotate
#declare transp = 0.0   // transparency,
                        // use 0.75 and you will see the sphere inside

camera
{
  location  <0, 1800, -1800>
  look_at   <0, 0, 0>
}

light_source{< -100, 200,-2000> color White}
light_source{<-1200,1200,-0000> color White}
light_source{< 1200,1200,-0000> color White}

background{LightBlue}


// vertices of the great stellated dodecahedron
#declare Vertex = array[33]
#declare Vertex[00] = <0,0,0>; // dummy. so count of the vertices starts
with 1
#declare Vertex[01] = <0, 0, 427>;
#declare Vertex[02] = <381.9, 0, 190.9>;
#declare Vertex[03] = <118, 363.2, 190.9>;
#declare Vertex[04] = <-309, 224.5, 190.9>;
#declare Vertex[05] = <-309, -224.5, 190.9>;
#declare Vertex[06] = <118, -363.2, 190.9>;
#declare Vertex[07] = <309, 224.5, -190.9>;
#declare Vertex[08] = <-118, 363.2, -190.9>;
#declare Vertex[09] = <-381.9, 0, -190.9>;
#declare Vertex[10] = <-118, -363.2, -190.9>;
#declare Vertex[11] = <309, -224.5, -190.9>;
#declare Vertex[12] = <0, 0, -427>;
#declare Vertex[13] = <500, 363.2, 809>;
#declare Vertex[14] = <-190.9, 587.7, 809>;
#declare Vertex[15] = <-618, 0, 809>;
#declare Vertex[16] = <-190.9, -587.7, 809>;
#declare Vertex[17] = <500, -363.2, 809>;
#declare Vertex[18] = <809, 587.7, 190.9>;
#declare Vertex[19] = <-309, 951, 190.9>;
#declare Vertex[20] = <-1000, 0, 190.9>;
#declare Vertex[21] = <-309, -951, 190.9>;
#declare Vertex[22] = <809, -587.7, 190.9>;
#declare Vertex[23] = <1000, 0, -190.9>;
#declare Vertex[24] = <309, 951, -190.9>;
#declare Vertex[25] = <-809, 587.7, -190.9>;
#declare Vertex[26] = <-809, -587.7, -190.9>;
#declare Vertex[27] = <309, -951, -190.9>;
#declare Vertex[28] = <190.9, -587.7, -809>;
#declare Vertex[29] = <618, 0, -809>;
#declare Vertex[30] = <190.9, 587.7, -809>;
#declare Vertex[31] = <-500, 363.2, -809>;
#declare Vertex[32] = <-500, -363.2, -809>;


#declare three= array[60][3] // all triangular faces
{
{13,1,2},{13,2,3},{13,3,1},{14,1,3},{14,3,4},{14,4,1},
{15,1,4},{15,4,5},{15,5,1},{16,1,5},{16,5,6},{16,6,1},
{17,1,6},{17,6,2},{17,2,1},{18,2,7},{18,7,3},{18,3,2},
{19,3,8},{19,8,4},{19,4,3},{20,4,9},{20,9,5},{20,5,4},
{21,5,10},{21,10,6},{21,6,5},{22,2,6},{22,6,11},{22,11,2},
{23,2,11},{23,11,7},{23,7,2},{24,3,7},{24,7,8},{24,8,3},
{25,4,8},{25,8,9},{25,9,4},{26,5,9},{26,9,10},{26,10,5},
{27,10,11},{27,11,6},{27,6,10},{28,10,12},{28,12,11},{28,11,10},
{29,11,12},{29,12,7},{29,7,11},{30,7,12},{30,12,6},{30,6,7},
{31,8,12},{31,12,9},{31,9,8},{32,12,10},{32,10,9},{32,9,12}
}


#declare Edge = array[90][2]
{
{1,2}, {2,3}, {1,3}, {2,7},
{3,7}, {2,11}, {7,11}, {11,12},
{7,12},{1,4}, {1,5}, {1,6},
{2,6}, {3,8}, {3,4}, {4,5},
{4,9}, {4,8},{5,6}, {5,10},
{5,9}, {6,10}, {6,11},
{7,8}, {8,9}, {8,12},
{9,10}, {9,12}, {10,11}, {10,12}
{13,1},{13,2},{13,3},{14,1},{14,3},{14,4},{15,1},{15,4},{15,5},
{16,1},{16,5},{16,6},{17,1},{17,6},{17,2},{18,2},{18,7},{18,3},
{19,3},{19,8},{19,4},{20,4},{20,9},{20,5},{21,5},{21,10},{21,6},
{22,2},{22,6},{22,11},{23,2},{23,11},{23,7},{24,3},{24,7},{24,8},
{25,4},{25,8},{25,9},{26,5},{26,9},{26,10},{27,10},{27,11},{27,6},
{28,10},{28,12},{28,11},{29,11},{29,12},{29,7},{30,7},{30,12},{30,6},
{31,8},{31,12},{31,9},{32,12},{32,10},{32,9}
}

#declare VertexU = union{
#declare i = 13;
#while(i<33)
        sphere{Vertex[i],5*re }
#declare i = i+1;
#end
}

#declare EdgeU = union{
#declare i = 0;
#while(i<90)
        cylinder{Vertex[Edge[i][0]],Vertex[Edge[i][1]],re
pigment{Black}}
#declare i = i+1;
#end
}

#declare FaceU = union{
#declare i = 0;
#while(i<60)
triangle{Vertex[three[i][0]],Vertex[three[i][1]],Vertex[three[i][2]]pigment{rgbt
<rand(s),rand(s),rand(s),transp> }}
#declare i = i+1;
#end
}


#declare Vertices = object{VertexU pigment{Red} rotate turn}
Vertices

#declare Faces = object{FaceU rotate turn}
Faces

#declare Edges = object{EdgeU rotate turn}
Edges

 sphere{Vertex[0] 300 rotate turn texture{Red_Marble scale 250}
finish{phong 1}}

Post a reply to this message

Richard Schorn wrote:
> 
> Enjoy!
> Richard Schorn
> 

Good. Interesting.
Do you have the two others ?

Post a reply to this message

there are three(!) others, but I computed only this one and the small
stellated dodecahedron.
When the Enlish translation  is ready, I will put the other one in this
NG.
BTW: the names of the polyhedra vary from book to book.

Regards
Richard Schorn

Post a reply to this message

Richard Schorn wrote:

> there are three(!) others, but I computed only this one and the small
> stellated dodecahedron.

<* swallowing the hook and the full line *>
I can only think of 3 stellated dodecahedrons... 
How do you construct them ? (especially the fourth ?)
Mine are extension of the surfaces(plane).

Example in 2D with a pentagon:
extending the lines give the pentalpha.
As there is only one additional point, there is only
one stellated pentagon.

For the dodecahedron, I can find up to 3 additionnal intersections,
thus 3 stellated dodecahedrons.
the fourth one is infinite and look like the merge of a lot
of pillars at the origin. As it is infinite, it is not 
a polyhedra (from my point of view).


> BTW: the names of the polyhedra vary from book to book.

Yes, I know that!

Post a reply to this message

you are perfectly right!!
When you wrote about "two others" I thought of "stellated" and you of
"dodecahedron".
The two stellated solids, discovered by Poinsot, are rather difficult to
compute!
Regards
Richard Schorn

Post a reply to this message

Richard Schorn wrote:

> you are perfectly right!!
> When you wrote about "two others" I thought of "stellated" and you of
> "dodecahedron".

Well, I was only thinking about the stellated solids based on the dodecahedron.

If you are ready to download about 450 k of images, have a look
 at http://www.crosswinds.net/~grimbert/pov/patch/kepler.html

(or disable autoloading of images before entering that page,
there is approx. twenty images, each between 4k and 62k )

I know I should split them among multiple pages, but I currently
lack time...

Post a reply to this message