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From: Dan Johnson
Subject: Polydoodle
Date: 23 Feb 2001 06:42:49
Message: <3A964E2F.C8EBA907@hotmail.com>
Couldn't find my math book today, so I went to a nearby university
library.  In addition to finding the answer to my question I also found
two books on polyhedra I had never seen before.  Decided to do a few
quick sketches.

--
Dan Johnson

http://www.geocities.com/zapob


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From: Dan Johnson
Subject: Re: Polydoodle
Date: 23 Feb 2001 06:46:48
Message: <3A964F0D.EDFBF5FE@hotmail.com>
Having trouble posting.  Posting several times instead


--
Dan Johnson

http://www.geocities.com/zapob


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polydoodle4.gif


 

From: Dan Johnson
Subject: Re: Polydoodle
Date: 23 Feb 2001 06:49:09
Message: <3A964F77.5610FB70@hotmail.com>
Saved the best for last


--
Dan Johnson

http://www.geocities.com/zapob


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From: Josh English
Subject: Re: Polydoodle
Date: 23 Feb 2001 07:37:54
Message: <3A9659F4.78A0091C@spiritone.com>
These are fun images. Would you mind explaining the basic method you used to
generate these? I can tell that the first on is genereated by boxes that are
rotated certain amounts, the second is built by tetrahedra, and the third by
octahedrons, but what about the specific rotations?

Josh

Dan Johnson wrote:

> Couldn't find my math book today, so I went to a nearby university
> library.  In addition to finding the answer to my question I also found
> two books on polyhedra I had never seen before.  Decided to do a few
> quick sketches.
>
> --
> Dan Johnson
>
> http://www.geocities.com/zapob
>
>   ------------------------------------------------------------------------
>  [Image]

--
Josh English -- Lexiphanic Lethomaniac
eng### [at] spiritonecom
The POV-Ray Cyclopedia http://www.spiritone.com/~english/cyclopedia/
"He who hebetates is last."


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From: Jérôme Grimbert
Subject: Re: Polydoodle
Date: 23 Feb 2001 07:39:49
Message: <3A965A62.A40CBD03@atosorigin.com>
Dan Johnson wrote:
> 
> Couldn't find my math book today, so I went to a nearby university
> library.  In addition to finding the answer to my question I also found
> two books on polyhedra I had never seen before.  Decided to do a few
> quick sketches.
> 
Welcome to the world of polyhedra :-)

Have also a look at thread titled "Kepler" (7 July 2000),
there is also some other polyhedra... not as colourfull as yours.


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From: yooper
Subject: Re: Polydoodle
Date: 23 Feb 2001 08:35:38
Message: <3a96672a@news.povray.org>
Interesting . . .
Went to yer site & snagged yer source zip . . . will have a look tonite.

There . . . you say:

*Yahoo Geocities doesn't allow unknown file types.
 So all source code has to be in zip files. *

I assume you mean .pov & .inc . . . ?
If so . . . try renaming them as .txt . . . that's what they are
and then anyone downloading them can change them back.
--
Y


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From: David Fontaine
Subject: Re: Polydoodle
Date: 23 Feb 2001 17:01:22
Message: <3A96DD50.8B1DA5B2@faricy.net>
Josh English wrote:

> These are fun images. Would you mind explaining the basic method you used to
> generate these? I can tell that the first on is genereated by boxes that are
> rotated certain amounts, the second is built by tetrahedra, and the third by
> octahedrons, but what about the specific rotations?

The tetrahedra and octahedra ones are stellations of the icosahedron. The cube
one probably has some properties you can use to find the rotations. The rest is
a matter trig or analytic geometry, so that's an issue of your own comfort with
mathematics... if you want I can explain some more.

--
David Fontaine  <dav### [at] faricynet>  ICQ 55354965
My raytracing gallery:  http://davidf.faricy.net/


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From: Anton Sherwood
Subject: Re: Polydoodle
Date: 23 Feb 2001 21:34:09
Message: <3A971DB7.2124F0F0@pobox.com>
David Fontaine wrote:
> The cube one probably has some properties you can use
> to find the rotations. . . .

See my response to "Nested Polyhedron", January 14.


(Peeve: slipping into `vi' mode for a moment, forgetting that i'm using
a generic GUI editor)

-- 
Anton Sherwood  --  br0### [at] p0b0xcom  --  http://ogre.nu/


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From: David Fontaine
Subject: Re: Polydoodle
Date: 23 Feb 2001 22:24:56
Message: <3A972927.C6E06CA4@faricy.net>
Anton Sherwood wrote:

> See my response to "Nested Polyhedron", January 14.

Thanks, but I already know that. What I mean is, the rotations are not
arbitrary; what determines them? (I see now that any pair of cubes share a
pair of opposing vertices in the first pic... as a logical consequence of
there being five of them the edges will form pentagrams, which I can see
too now...)

--
David Fontaine  <dav### [at] faricynet>  ICQ 55354965
My raytracing gallery:  http://davidf.faricy.net/


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From: Dan Johnson
Subject: Re: Polydoodle
Date: 24 Feb 2001 06:36:30
Message: <3A979E4B.F39B1CD5@hotmail.com>
Well each of them is a combination of five shapes rotated around the center of
a face of a dodecahedron.  There were other interesting rotations in that
book, couldn't remember them when I got home though.  I will have to go back
to that library soon.  Source is below, get macros2.inc from David Fontaine's
page, and polyhedra,inc from my page.

> --
> David Fontaine  <dav### [at] faricynet>  ICQ 55354965
> My raytracing gallery:  http://davidf.faricy.net/

#include "colors.inc"
#include "polyhedra.inc"
#include "macros2.inc"
#include "finish.inc"

global_settings { max_trace_level 20 }
light_source { <3,20,-40> rgb 2}
camera {location <0,0,-20> look_at 0 angle 20}

background {White}

#declare Tex = array[5] {Red,Orange,Yellow,Green,Blue}
#declare F = rgbft <0,0,0,.7,.7>

#declare Tet = union {
        Tetrahedron_edges(1,.1)
        Tetrahedron_vertexes(1,.1)
        }
#declare Tet2 = object {Tetrahedron_faces}

#declare Tets =
union {
        object {Tet pigment {Tex[0]}}
        object {Tet pigment {Tex[1]} arotate(Icosahedron1,72)}
        object {Tet pigment {Tex[2]} arotate(Icosahedron1,(2*72))}
        object {Tet pigment {Tex[3]} arotate(Icosahedron1,3*72)}
        object {Tet pigment {Tex[4]} arotate(Icosahedron1,4*72)}

        object {Tet2 pigment {Tex[0]+F}}
        object {Tet2 pigment {Tex[1]+F} arotate(Icosahedron1,72)}
        object {Tet2 pigment {Tex[2]+F} arotate(Icosahedron1,(2*72))}
        object {Tet2 pigment {Tex[3]+F} arotate(Icosahedron1,3*72)}
        object {Tet2 pigment {Tex[4]+F} arotate(Icosahedron1,4*72)}
        finish {Shiny}
        }

#declare Cub = object {Cube_edges(1,.1)}
#declare Cub2 = object {Cube_faces}

#declare Cubs =
union {
        object {Cub pigment {Tex[0]}}
        object {Cub pigment {Tex[1]} arotate(Icosahedron1,72)}
        object {Cub pigment {Tex[2]} arotate(Icosahedron1,2*72)}
        object {Cub pigment {Tex[3]} arotate(Icosahedron1,3*72)}
        object {Cub pigment {Tex[4]} arotate(Icosahedron1,4*72)}
        rotate 45*y
        }
#declare Cubs2 =
union {
        object {Cub2 pigment {Tex[0]}}
        object {Cub2 pigment {Tex[1]} arotate(Icosahedron1,72)}
        object {Cub2 pigment {Tex[2]} arotate(Icosahedron1,2*72)}
        object {Cub2 pigment {Tex[3]} arotate(Icosahedron1,3*72)}
        object {Cub2 pigment {Tex[4]} arotate(Icosahedron1,4*72)}
        rotate 45*y
        finish {Shiny}
        }
#declare Oct = union {
        Octahedron_edges(Golden,.08)
        Octahedron_vertexes(Golden,.08)
        }
#declare Oct2 = object {Octahedron_faces}

#declare Octs =
union {
        object {Oct pigment {Tex[0]}}
        object {Oct pigment {Tex[1]} arotate(Icosahedron1,72)}
        object {Oct pigment {Tex[2]} arotate(Icosahedron1,2*72)}
        object {Oct pigment {Tex[3]} arotate(Icosahedron1,3*72)}
        object {Oct pigment {Tex[4]} arotate(Icosahedron1,4*72)}
        rotate 45*y
        finish {Shiny}
        }
//#declare Octs2 =
union {
        object {Oct2 pigment {Tex[0]}}
        object {Oct2 pigment {Tex[1]} arotate(Icosahedron1,72)}
        object {Oct2 pigment {Tex[2]} arotate(Icosahedron1,2*72)}
        object {Oct2 pigment {Tex[3]} arotate(Icosahedron1,3*72)}
        object {Oct2 pigment {Tex[4]} arotate(Icosahedron1,4*72)}
        rotate 45*y
        finish {Shiny}
        }



--
Dan Johnson

http://www.geocities.com/zapob


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