How can I build a looking-like sphere using triangles?
For those of you who played D&D, I mean the 20 faced dice, for example.

All triangles that build the sphere must be all equal in their area, and
all of their angles are 60 degrees.
An image would explain better:

[Image]

Moderators: I have devastatedly compressed the image to 7.5 kb,
I hope you don't mind that I have included a file.

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If you mean only the external object built from triangles: it's a
regular icosahedron. The internal object is an regular dodecahedron (the
dual polyhedron of a icosahedron).
Approximating a sphere by equilateral triangles is only possible in 3
ways: a regular tetrahedron, a regular octahedron or a regular
icosahedron. Of course the icosahedron is the best approximation.
If not all triangles have to be congruent there are different ways to
construct a "dome".
Have a look on my website for regular polyhedra and if you want an
appropriate include file, let me know (of course you can find polyhedron
include files on the web).
Herman

Eitan Tal wrote:
> 
> How can I build a looking-like sphere using triangles?
> For those of you who played D&D, I mean the 20 faced dice, for
> example.
> 
> All triangles that build the sphere must be all equal in their area,
> and all of their angles are 60 degrees.
> An image would explain better:
> 
> [Image]
> 
> Moderators: I have devastatedly compressed the image to 7.5 kb,
> I hope you don't mind that I have included a file.

-- 
Herman Serras
Gent (Belgium)
http://cage.rug.ac.be/~hs/

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Thanks!
and Yes, I mean the External object.
Please tell me more about how to constuct a dome.


Herman Serras wrote:

> If you mean only the external object built from triangles: it's a
> regular icosahedron. The internal object is an regular dodecahedron (the
> dual polyhedron of a icosahedron).
> Approximating a sphere by equilateral triangles is only possible in 3
> ways: a regular tetrahedron, a regular octahedron or a regular
> icosahedron. Of course the icosahedron is the best approximation.
> If not all triangles have to be congruent there are different ways to
> construct a "dome".
> Have a look on my website for regular polyhedra and if you want an
> appropriate include file, let me know (of course you can find polyhedron
> include files on the web).
> Herman
>
> Eitan Tal wrote:
> >
> > How can I build a looking-like sphere using triangles?
> > For those of you who played D&D, I mean the 20 faced dice, for
> > example.
> >
> > All triangles that build the sphere must be all equal in their area,
> > and all of their angles are 60 degrees.
> > An image would explain better:
> >
> > [Image]
> >
> > Moderators: I have devastatedly compressed the image to 7.5 kb,
> > I hope you don't mind that I have included a file.
>
> --
> Herman Serras
> Gent (Belgium)
> http://cage.rug.ac.be/~hs/

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Take a look at:
http://www.cris.com/~rjbono/html/domes.html
Output to PovRay is a possibility.
Greetings,
Herman

Eitan Tal wrote:
> 
> Thanks!
> and Yes, I mean the External object.
> Please tell me more about how to constuct a dome.
> 
> Herman Serras wrote:
> 
> > If you mean only the external object built from triangles: it's a
> > regular icosahedron. The internal object is an regular dodecahedron (the
> > dual polyhedron of a icosahedron).
> > Approximating a sphere by equilateral triangles is only possible in 3
> > ways: a regular tetrahedron, a regular octahedron or a regular
> > icosahedron. Of course the icosahedron is the best approximation.
> > If not all triangles have to be congruent there are different ways to
> > construct a "dome".
> > Have a look on my website for regular polyhedra and if you want an
> > appropriate include file, let me know (of course you can find polyhedron
> > include files on the web).
> > Herman
> >
> > Eitan Tal wrote:
> > >
> > > How can I build a looking-like sphere using triangles?
> > > For those of you who played D&D, I mean the 20 faced dice, for
> > > example.
> > >
> > > All triangles that build the sphere must be all equal in their area,
> > > and all of their angles are 60 degrees.
> > > An image would explain better:
> > >
> > > [Image]
> > >
> > > Moderators: I have devastatedly compressed the image to 7.5 kb,
> > > I hope you don't mind that I have included a file.
> >
> > --
> > Herman Serras
> > Gent (Belgium)
> > http://cage.rug.ac.be/~hs/

-- 
Herman Serras
Gent (Belgium)
http://cage.rug.ac.be/~hs/

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You know the rules for binary attachments and HTML in these groups, don't 
you?  Please cancel this post and if post the image in p.b.images.

----------
In article <3BB18F22.C5CA799F@netvision.net.il>, Eitan Tal
<eit### [at] netvisionnetil> wrote:

Message-ID: <3BB18F22.C5CA799F@netvision.net.il>
Date: Wed, 26 Sep 2001 10:17:39 +0200
From: Eitan Tal <eit### [at] netvisionnetil>
Newsgroups: povray.general
Subject: Geometry Question:
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