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5 Nov 2024 11:18:54 EST (-0500)
  Vertices of a Icosahedron (Message 1 to 6 of 6)  
From: Mick Hazelgrove
Subject: Vertices of a Icosahedron
Date: 5 Oct 1998 13:45:05
Message: <01bdf07f$81754120$ec3da8c2@wphnvffu>
Help

How can I calculate the 3D positions of the vertices of an Icosahedron

Thanks in advance

Mick Hazelgrove


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From: Ken
Subject: Re: Vertices of a Icosahedron
Date: 5 Oct 1998 18:35:46
Message: <36193B51.50517A49@pacbell.net>
Mick Hazelgrove wrote:

> Help
> How can I calculate the 3D positions of the vertices of an Icosahedron
> Thanks in advance
>
> Mick Hazelgrove

Will this work for you ?

  -- 20 triangular faces 12 vertices 30 edges
icosa1   0.0000000000E+00  0.0000000000E+00  3.8042260652E-01
icosa2   3.4026032334E-01  0.0000000000E+00  1.7013016167E-01
icosa3   1.0514622242E-01  3.2360679775E-01  1.7013016167E-01
icosa4  -2.7527638409E-01  2.0000000000E-01  1.7013016167E-01
icosa5  -2.7527638410E-01 -2.0000000000E-01  1.7013016167E-01
icosa6   1.0514622242E-01 -3.2360679775E-01  1.7013016167E-01
icosa7   2.7527638409E-01  2.0000000000E-01 -1.7013016167E-01
icosa8  -1.0514622242E-01  3.2360679775E-01 -1.7013016167E-01
icosa9  -3.4026032334E-01  1.2378598452E-12 -1.7013016167E-01
icosa10 -1.0514622243E-01 -3.2360679775E-01 -1.7013016167E-01
icosa11  2.7527638409E-01 -2.0000000000E-01 -1.7013016167E-01
icosa12  0.0000000000E+00  0.0000000000E+00 -3.8042260652E-01

EndPointList Name X Y Z

Ken Tyler


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From: Michael Andrews
Subject: Re: Vertices of a Icosahedron
Date: 6 Oct 1998 07:59:11
Message: <3619F807.12343958@remove-this.reading.ac.uk>
I was wanting exactly the same thing. I found these coords in John
VanSickle's rock generator and extracted them to a PoV array as follows:

#declare qA=(sqrt(5)+1)/4;
#declare qB=0.5/sqrt(qA*qA+1/4);
#declare qA=qA/sqrt(qA*qA+1/4);

#declare P = array[12] {
 < qA, qB,0>,
 <-qA, qB,0>,
 < qA,-qB,0>,
 <-qA,-qB,0>,
 <0, qA, qB>,
 <0,-qA, qB>,
 <0, qA,-qB>,
 <0,-qA,-qB>,
 < qB,0, qA>,
 < qB,0,-qA>,
 <-qB,0, qA>,
 <-qB,0,-qA>
}

    Hope this helps,
        Mike Andrews.

Mick Hazelgrove wrote:

> Help
>
> How can I calculate the 3D positions of the vertices of an Icosahedron
>
> Thanks in advance
>
> Mick Hazelgrove


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From: JK
Subject: Re: Vertices of a Icosahedron
Date: 8 Oct 1998 18:37:21
Message: <361d3091.0@news.povray.org>
>icosa1   0.0000000000E+00  0.0000000000E+00
3.8042260652E-01
>icosa2   3.4026032334E-01  0.0000000000E+00
1.7013016167E-01
>icosa3   1.0514622242E-01  3.2360679775E-01
1.7013016167E-01
>icosa4  -2.7527638409E-01  2.0000000000E-01
1.7013016167E-01
  <and so on>


Just wondering.... How did you do that? The precision is
impressive.

Julius Klatte
http://surf.to/jkhome
http://surf.to/UAGalleries


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From: Ken
Subject: Re: Vertices of a Icosahedron
Date: 8 Oct 1998 19:13:23
Message: <361D38DE.D58A472@pacbell.net>
JK wrote:

> >icosa1   0.0000000000E+00  0.0000000000E+00
> 3.8042260652E-01
> >icosa2   3.4026032334E-01  0.0000000000E+00
> 1.7013016167E-01
> >icosa3   1.0514622242E-01  3.2360679775E-01
> 1.7013016167E-01
> >icosa4  -2.7527638409E-01  2.0000000000E-01
> 1.7013016167E-01
>   <and so on>
>
> Just wondering.... How did you do that? The precision is
> impressive.
>
> Julius Klatte
> http://surf.to/jkhome
> http://surf.to/UAGalleries

  I can't remember what the source of this was. I believe it
came from a university majors' work on crystographically
correct polyhydra.

Ken Tyler


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From: Nieminen Mika
Subject: Re: Vertices of a Icosahedron
Date: 9 Oct 1998 09:07:29
Message: <361dfc81.0@news.povray.org>
JK <jkl### [at] geocitiescom> wrote:
: Just wondering.... How did you do that? The precision is
: impressive.

  Those vertices can be calculated analytically (ie. you can write an exact
equation describing a vertex of the icosahedron). Then you can just calculate
a numerical value with any precision you want (and your calculator supports).

-- 
                                                           - Warp. -


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