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Hello,
I've been looking for the planes that define a rhombic triacontahedron. So
far I've found the below. Does anyone have a similiar declaration for a rhombic
triacontahedron?
http://mathworld.wolfram.com/RhombicTriacontahedron.html
I want the planes of the rhombic triacontahedron to match the edges of the
dodecahedron defined below as I'm wanting to animate an edge twist dodecahedron
like those seen here:
http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/
Thanks,
Carl
#declare Dodecahedron =
intersection
{plane {-z, 1 rotate <-26.56505117708, 0, 0>}
plane {-z, 1 rotate <-26.56505117708, -72, 0>}
plane {-z, 1 rotate <-26.56505117708, -144, 0>}
plane {-z, 1 rotate <-26.56505117708, -216, 0>}
plane {-z, 1 rotate <-26.56505117708, -288, 0>}
plane {-z, 1 rotate <26.56505117708, -36, 0>}
plane {-z, 1 rotate <26.56505117708, -108, 0>}
plane {-z, 1 rotate <26.56505117708, -180, 0>}
plane {-z, 1 rotate <26.56505117708, -252, 0>}
plane {-z, 1 rotate <26.56505117708, -324, 0>}
plane { y, 1}
plane {-y, 1}
bounded_by {sphere {0, 1.2585}}
}
#declare RhombicDodecahedron =
intersection
{
plane { z, 1 rotate < 0, 45, 45>}
plane { z, 1 rotate < 0, 45, -45>}
plane { z, 1 rotate < 0, -45, 45>}
plane { z, 1 rotate < 0, -45, -45>}
plane {-z, 1 rotate < 0, 45, 45>}
plane {-z, 1 rotate < 0, 45, -45>}
plane {-z, 1 rotate < 0, -45, 45>}
plane {-z, 1 rotate < 0, -45, -45>}
plane {-x, 1 }
plane { x, 1 }
plane { y, 1}
plane {-y, 1}
}
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I believe this does it...
#declare RhombicTriacontahedron =
intersection
{plane {-z, 1 rotate <58.28252558854, -36, 0>}
plane {-z, 1 rotate <58.28252558854, -108, 0>}
plane {-z, 1 rotate <58.28252558854, -180, 0>}
plane {-z, 1 rotate <58.28252558854, -252, 0>}
plane {-z, 1 rotate <58.28252558854, -324, 0>}
plane {z, 1 rotate <58.28252558854, -36, 0>}
plane {z, 1 rotate <58.28252558854, -108, 0>}
plane {z, 1 rotate <58.28252558854, -180, 0>}
plane {z, 1 rotate <58.28252558854, -252, 0>}
plane {z, 1 rotate <58.28252558854, -324, 0>}
plane {-y, 1 rotate <58.28252558854, -36, 0>}
plane {-y, 1 rotate <58.28252558854, -108, 0>}
plane {-y, 1 rotate <58.28252558854, -180, 0>}
plane {-y, 1 rotate <58.28252558854, -252, 0>}
plane {-y, 1 rotate <58.28252558854, -324, 0>}
plane {y, 1 rotate <58.28252558854, -36, 0>}
plane {y, 1 rotate <58.28252558854, -108, 0>}
plane {y, 1 rotate <58.28252558854, -180, 0>}
plane {y, 1 rotate <58.28252558854, -252, 0>}
plane {y, 1 rotate <58.28252558854, -324, 0>}
plane {-x, 1 rotate <58.28252558854, -36, 0>}
plane {-x, 1 rotate <58.28252558854, -108, 0>}
plane {-x, 1 rotate <58.28252558854, -180, 0>}
plane {-x, 1 rotate <58.28252558854, -252, 0>}
plane {-x, 1 rotate <58.28252558854, -324, 0>}
plane {x, 1 rotate <58.28252558854, -36, 0>}
plane {x, 1 rotate <58.28252558854, -108, 0>}
plane {x, 1 rotate <58.28252558854, -180, 0>}
plane {x, 1 rotate <58.28252558854, -252, 0>}
plane {x, 1 rotate <58.28252558854, -324, 0>}
}
Looks good to me... wasn't as complicated as I was expecting.
Carl
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Carl <car### [at] gmail com> wrote:
> #declare RhombicTriacontahedron =
> intersection
> {plane {-z, 1 rotate <58.28252558854, -36, 0>}
> plane {-z, 1 rotate <58.28252558854, -108, 0>}
> plane {-z, 1 rotate <58.28252558854, -180, 0>}
> plane {-z, 1 rotate <58.28252558854, -252, 0>}
> plane {-z, 1 rotate <58.28252558854, -324, 0>}
> plane {z, 1 rotate <58.28252558854, -36, 0>}
> plane {z, 1 rotate <58.28252558854, -108, 0>}
> plane {z, 1 rotate <58.28252558854, -180, 0>}
> plane {z, 1 rotate <58.28252558854, -252, 0>}
> plane {z, 1 rotate <58.28252558854, -324, 0>}
> plane {-y, 1 rotate <58.28252558854, -36, 0>}
> plane {-y, 1 rotate <58.28252558854, -108, 0>}
> plane {-y, 1 rotate <58.28252558854, -180, 0>}
> plane {-y, 1 rotate <58.28252558854, -252, 0>}
> plane {-y, 1 rotate <58.28252558854, -324, 0>}
> plane {y, 1 rotate <58.28252558854, -36, 0>}
> plane {y, 1 rotate <58.28252558854, -108, 0>}
> plane {y, 1 rotate <58.28252558854, -180, 0>}
> plane {y, 1 rotate <58.28252558854, -252, 0>}
> plane {y, 1 rotate <58.28252558854, -324, 0>}
> plane {-x, 1 rotate <58.28252558854, -36, 0>}
> plane {-x, 1 rotate <58.28252558854, -108, 0>}
> plane {-x, 1 rotate <58.28252558854, -180, 0>}
> plane {-x, 1 rotate <58.28252558854, -252, 0>}
> plane {-x, 1 rotate <58.28252558854, -324, 0>}
> plane {x, 1 rotate <58.28252558854, -36, 0>}
> plane {x, 1 rotate <58.28252558854, -108, 0>}
> plane {x, 1 rotate <58.28252558854, -180, 0>}
> plane {x, 1 rotate <58.28252558854, -252, 0>}
> plane {x, 1 rotate <58.28252558854, -324, 0>}
> }
How about:
#macro RhombicTriacontahedronSection(Dir)
plane {Dir, 1 rotate <58.28252558854, -36, 0>}
plane {Dir, 1 rotate <58.28252558854, -108, 0>}
plane {Dir, 1 rotate <58.28252558854, -180, 0>}
plane {Dir, 1 rotate <58.28252558854, -252, 0>}
plane {Dir, 1 rotate <58.28252558854, -324, 0>}
#end
#declare RhombicTriacontahedron =
intersection
{ RhombicTriacontahedronSection(-z)
RhombicTriacontahedronSection(z)
RhombicTriacontahedronSection(-y)
RhombicTriacontahedronSection(y)
RhombicTriacontahedronSection(-x)
RhombicTriacontahedronSection(x)
};
--
- Warp
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I generated some files which might be useful for you,
givin a mesh2 object of the desired shape, a skeleton made of cylinder, and
lists of transformations that map an object to either a edge or a face of the
polyhedron :
dodecahedron :
http://code.google.com/p/spirals/source/browse/pearls/scene/geometry/polyhedra/archimedean/dodecahedron.inc
rhombic triacontahedron :
http://code.google.com/p/spirals/source/browse/pearls/scene/geometry/polyhedra/archimedean/rhombic_triacontahedron.inc
Other polyhedra are available in the same directory.
The ugly java source code generating those inc from off files can be
found there :
http://code.google.com/p/voronoijava/source/browse/Voronoi/src/test/OffReader3DMeshV2.java
(some classes usefull there are in the utils directory)
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I almost replied to this before, but I wasn't sure if I would be of any help
(and then you solved your query anyway ;-), but if you look in the object
collection:
http://lib.povray.org/searchcollection/index2.php
You can see my recent platonic, archimedean and catalan solid mesh2 include
files (I have others to be added in the near future). Although I don't have any
mapping transforms in my includes, they do supply all the vertices in an array,
in addition to the meshes.
"fdecomite" <nomail@nomail> wrote:
> dodecahedron :
>
http://code.google.com/p/spirals/source/browse/pearls/scene/geometry/polyhedra/archimedean/dodecahedron.inc
>
> rhombic triacontahedron :
>
http://code.google.com/p/spirals/source/browse/pearls/scene/geometry/polyhedra/archimedean/rhombic_triacontahedron.in
c
<harmless pedantry>
.... and of course you knew that neither the dodecahedron nor the rhombic
triacontahedron are archimedean solids :-)
</harmless pedantry>
Bill
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> <harmless pedantry>
> .... and of course you knew that neither the dodecahedron nor the rhombic
> triacontahedron are archimedean solids :-)
> </harmless pedantry>
I always have messy directories...
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