Take the plane of one face of an icosahedron and intersect it with all
the other planes. Use the resulting lines to divide this plane into 67
sectors. "Fill in" certain combinations of these sectors and use them as
one face on the icosahedron, then copy it and rotate it into place for
the other faces. (There are 59 such combinations, this is only a select
few.)
The trig should only take you all day, but then again, you enjoyed it,
you're a flaming math nerd, aren't you? :-)

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 | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
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"Sitting on a cornflake, waiting for the van to come" -Beatles

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Attachments:
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Preview of image '59ico.jpg'

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Preview of image '05ico.jpg'

Preview of image '08ico.jpg'

Preview of image '09ico.jpg'

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Preview of image '17ico.jpg'

Preview of image '22ico.jpg'

Preview of image '31ico.jpg'

Preview of image '39ico.jpg'

Preview of image '01ico.jpg'

It would be interesting to render these at desktop picture size, and 
have the computer select one randomly at each startup...

-- 
Chris Huff
e-mail: chr### [at] yahoocom
Web page: http://chrishuff.dhs.org/

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Berry nice.

I'm not a flaming math nerd, I only wish I was.

I will question your texture.

Lame.Lame.Lame.

Peter Warren
war### [at] hotmailcom

"Strawberry fields forever"

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Peter Warren wrote:

> Lame.Lame.Lame.

Yeah, I know.
T_Stone14.T_Stone14.T_Stone14

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___     ______________________________________________________
 | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
 |_/avid |ontaine               http://www.faricy.net/~davidf/

"Sitting on a cornflake, waiting for the van to come" -Beatles

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David Fontaine wrote in message <38B1ACA5.8F9D8F79@faricy.net>...
>Take the plane of one face of an icosahedron and intersect it with all
>the other planes. Use the resulting lines to divide this plane into 67
>sectors. "Fill in" certain combinations of these sectors and use them as
>one face on the icosahedron, then copy it and rotate it into place for
>the other faces. (There are 59 such combinations, this is only a select
>few.)

OK, Simplify that please <grin>

>The trig should only take you all day, but then again, you enjoyed it,
>you're a flaming math nerd, aren't you? :-)


i used to be, but maths skills have gone unused since Physics 3 (two years
ago) and I'm rusty.


Any chance of some code?

Gail
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Gail Shaw wrote in message <38b38881@news.povray.org>...
>Any chance of some code?
This code is well known.

//******************** Stellation of the Icoasahedron *********************
//*************************  All 59 possible ******************************
//********************** John Cranmer June 1995 ***************************
//*************** Thanks to Grant Hutchinson and Tom Gettys ***************
//************************ Joh### [at] jacydemoncouk **************************

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Gail Shaw wrote:

> Any chance of some code?

My code would be useless because I calculated all the intersection points
outside of POV and just pasted in the final result. But I did find a nice way
to store all the possibilities:
#declare Pt=array[n]{All the points of intersection}
#declare Sc=array[n][3]{Points which enclose each triangular "sector"}
#declare Sectors01=array[n]{All "sectors" included in stellation 1}
...
#declare Sectors59=array[n]{All "sectors" included in stellation 59}

then call a macro, StellatedIcosahedron(SectorsN), which places all the mesh
stuff.
There is almost surely a more efficient way than what I did (for certain
reasons), but this works fine for me.

--
___     ______________________________________________________
 | \     |_                 <dav### [at] faricynet> <ICQ 55354965>
 |_/avid |ontaine               http://www.faricy.net/~davidf/

"Sitting on a cornflake, waiting for the van to come" -Beatles

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