I've been flitting from project to project quite a bit lately, not really had
the time to devote to intensive problem-solving. So here's some fruit from a
'lightweight tinkering' project I've started recently - to produce a relatively
comprehensive library of polyhedra macros. I've settled on two macros per
polyhedron - one for faces, one for edges - allowing different textures for
different polygons, for edge cylinders and vertex spheres. I've also added a
flag to make the polyhedron sit on the x-z plane, on its largest type of face
(or, in the case of the stellated forms, on three points).

These are the Kepler-Poinsot polyhedra, from left to right:
Great stellated dodecahedron
Small stellated dodecahedron
Great icosahedron
Great dodecahedron

The macros are generated automatically by a python script, reading the vertices
and face indices from the .wrl files on George Hart's VR polyhedra site:

http://www.georgehart.com/virtual-polyhedra/vp.html

The stellations need hand-tweaking to get the plane alignment right, but
otherwise it's quite a painless process (once I'd got the conversion program
working, anyway!)

Bill

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Attachments:
Download 'kepler-poinsot.jpg' (198 KB)

Preview of image 'kepler-poinsot.jpg'

The stellated edge-only forms remind me of a toy I got as a child from 
the Science Museum of Minnesota - I wonder if I still have it, in fact.  
It was a kit for building shapes like this, with vaguely star-shaped (6-
pointed IIRC) rubber caps that you could insert clear plastic rods into 
in order to make various shapes.

Might be time to rummage around in the basement to see if it's in a box 
somewhere.

Jim

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Looking good, Bill.

Reminds me of the little plugin in Moray  :-)

Thomas

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Jim Henderson <nos### [at] nospamcom> wrote:
> The stellated edge-only forms remind me of a toy I got as a child from
> the Science Museum of Minnesota - I wonder if I still have it, in fact.
> It was a kit for building shapes like this, with vaguely star-shaped (6-
> pointed IIRC) rubber caps that you could insert clear plastic rods into
> in order to make various shapes.
>
> Might be time to rummage around in the basement to see if it's in a box
> somewhere.

I used to have some of these when I was young:

http://www.polydron.co.uk/

And the geomag-type toys are pretty good for polyhedra too:

http://en.wikipedia.org/wiki/Geomag

And my dad had a large collection of the platonic/archimedean solids that he'd
built from breakfast cereal boxes.

I think in many ways my interest in geometry and raytracing was inevitable... :)

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"Thomas de Groot" <tDOTdegroot@interDOTnlANOTHERDOTnet> wrote:
> Looking good, Bill.
>
> Reminds me of the little plugin in Moray  :-)

I didn't know about that - I don't really use Moray. Does it do a wide range of
polyhedra, or just the basics?

So far I've got the Platonic, Archimedean, Catalan and Kepler-Poinsot solids.
I'm going to start on the Johnson solids over the next day or so, then maybe
have a crack at the stellations of the icosahedron.

:-)

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"Bill Pragnell" <bil### [at] hotmailcom> schreef in bericht 
news:web.4a34f9b09ec74c6f69f956610@news.povray.org...
>
> I didn't know about that - I don't really use Moray. Does it do a wide 
> range of
> polyhedra, or just the basics?
>
> So far I've got the Platonic, Archimedean, Catalan and Kepler-Poinsot 
> solids.
> I'm going to start on the Johnson solids over the next day or so, then 
> maybe
> have a crack at the stellations of the icosahedron.
>

Just the basics, I guess (been a long while).

The plugin is polyhedre.lua (FullMoon) and last I used it (about 2005) I 
made octahedron, icosahedron, dodecahedron, tetrahedron with it. I am trying 
to find a tutorial somewhere... Maybe you remember my Kepler image (probably 
not) back in that year.

Thomas

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My excuses. Correction to my answer. It is the Domer plugin which makes the 
Euclidian primitives, not polyheder.lua.

Thomas

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On Sun, 14 Jun 2009 09:13:38 -0400, Bill Pragnell wrote:

> Jim Henderson <nos### [at] nospamcom> wrote:
>> The stellated edge-only forms remind me of a toy I got as a child from
>> the Science Museum of Minnesota - I wonder if I still have it, in fact.
>> It was a kit for building shapes like this, with vaguely star-shaped
>> (6- pointed IIRC) rubber caps that you could insert clear plastic rods
>> into in order to make various shapes.
>>
>> Might be time to rummage around in the basement to see if it's in a box
>> somewhere.
> 
> I used to have some of these when I was young:
> 
> http://www.polydron.co.uk/
> 
> And the geomag-type toys are pretty good for polyhedra too:
> 
> http://en.wikipedia.org/wiki/Geomag
> 
> And my dad had a large collection of the platonic/archimedean solids
> that he'd built from breakfast cereal boxes.
> 
> I think in many ways my interest in geometry and raytracing was
> inevitable... :)

Cool toys - I got to thinking about this more, and the kit that I had 
didn't include instructions for stellated forms (all the plastic segments 
were the same length, so designs where the segments pass through the 
object wouldn't work at all).  The result was similar to the Geomag 
results but there were no magnets.

Jim

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"Bill Pragnell" <bil### [at] hotmailcom> wrote:
> I'm going to start on the Johnson solids over the next day or so, then maybe
> have a crack at the stellations of the icosahedron.

Wowee, just been reading a bit about the stellations of the icosahedron. These
shapes are awesome. I can't wait to start firing photons at these bad boys!

http://en.wikipedia.org/wiki/The_fifty_nine_icosahedra

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On Sat, 13 Jun 2009 13:02:22 EDT, "Bill Pragnell"
<bil### [at] hotmailcom> wrote:

>I've been flitting from project to project quite a bit lately, not really had
>the time to devote to intensive problem-solving. So here's some fruit from a
>'lightweight tinkering' project I've started recently - to produce a relatively
>comprehensive library of polyhedra macros. I've settled on two macros per
>polyhedron - one for faces, one for edges - allowing different textures for
>different polygons, for edge cylinders and vertex spheres. I've also added a
>flag to make the polyhedron sit on the x-z plane, on its largest type of face
>(or, in the case of the stellated forms, on three points).
>
>These are the Kepler-Poinsot polyhedra, from left to right:
>Great stellated dodecahedron
>Small stellated dodecahedron
>Great icosahedron
>Great dodecahedron
>
>The macros are generated automatically by a python script, reading the vertices
>and face indices from the .wrl files on George Hart's VR polyhedra site:
>
>http://www.georgehart.com/virtual-polyhedra/vp.html
>
>The stellations need hand-tweaking to get the plane alignment right, but
>otherwise it's quite a painless process (once I'd got the conversion program
>working, anyway!)
>
>Bill


You may want to have a look at "Great Stella" a shareware app that
will do amazing things with polyhedra and also have a POV export
function.

John

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