Request: Geometric Solids

In article <338...@garnet.fsu.edu>, 
Michael Naylor <mna...@garnet.fsu.edu> writes:
>The Platonic, or 
>perfect, solids are those five shapes with every face a regular polygon, 
>and having the same number of edges meeting at each vertex... otherwise 
>known as "D & D dice".

Omigawd. Remind me:  terahedron (three triangles meet at each vertex),
cube (four squares meet at each vertex),  and...  Dodecahedron
and Icosahedron, one is converse to the other i.e. got by drawing a dot
for the centre of each face of the other, then that thing with 60
vertices like the drawing on a football.  Hmm.  Yes, they might be
a bit awkward to draw in ascii. 

                                            |~/           |~/
~~|;'^';-._.-;'^';-._.-;'^';-._.-;'^';-._.-;||';-._.-;'^';||_.-;'^'0-|~~
P |      Woof Woof, Glug Glug               ||____________||      0  | P
O |   Who Drowned the Judge's Dog?          | . . . . . . . '----. 0 | O
O |         answers on                  *---|_______________  @__o0  | O
L |_<a href="news:alt.religion.scientology">________________|/_______| L
 and<a href="http://www.xemu.demon.co.uk/clam/lynx/q0.html">

In article <338...@garnet.fsu.edu>, 
Michael Naylor <mna...@garnet.fsu.edu> writes:
>The Platonic, or 
>perfect, solids are those five shapes with every face a regular polygon, 
>and having the same number of edges meeting at each vertex... otherwise 
>known as "D & D dice".

Dave Bird Writes:

Omigawd. Remind me:  terahedron (three triangles meet at each vertex),
cube (four squares meet at each vertex),  and...  Dodecahedron
and Icosahedron, one is converse to the other i.e. got by drawing a dot
for the centre of each face of the other, then that thing with 60
vertices like the drawing on a football.  Hmm.  Yes, they might be
a bit awkward to draw in ascii. 

<cool sig cut.>

Here they are:

Tetrahedron:  Four triangular sides, a pyramid with a triangular base
(unlike the Egyptian pyramids, which have square bases)

Cube:  A cube.  You, know, six squares, a box.

Octahedron:  Eight triangular faces, meeting four at a corner.  Picture
two Eygtian pyramids stuck bottom-to-bottom.

Dodecahedron:  Twelve pentagonal faces.  Sheesh, if you thought drawing
a pentacle was tough...  The pentagons meet three to a corner.

Icosahedron:  Twenty triangular faces, meeting five at a corner.  Can't
think of anything you might have seen before with this shape.  It's sort
of reminiscent of Epcot, but Epcot is a geodesic dome with hundreds of
faces.

The 60-vertex monster you're talking about is a truncated icosahedron...
that is, an icosahedron with the corners clipped.  Each triangular face
becomes a hexagon (corners clipped), and at each vertex, where five
triangles used to meet, is a pentagon.  There are, therefore, 20
hexagons, 12 pentagons, and yes, 60 vertices.  This is indeed, a
football (or "soccer ball" as we say in the States), and there is even a
carbon molecule formed this way known as the "Buckey Ball" after its
discoverer, Buckminster Fuller.

Anyways, yes, making these shapes in ASCII is a real challenge.  Any
takers?

Michael

 ----       __  __ () _ _ __    __  _  _ __ __   ___ ___       o      
| \_|_\    |  \/  |--| '(| =|  |  \| |/o \ " /|_/ O | O )        ()  o
|_|_| |    |_\__/_|__|_|_|__|  |_|\__|_/\_|_|___|__/|_\_\     o_/||\/ 
 \|__\|  Michael Naylor, mna...@math.fsu.edu, (904) 644-8433   _/\_

> 
> Anyways, yes, making these shapes in ASCII is a real challenge.  Any
> takers?
> 


How about posting the URLs to some pictures... (I got the first three
but then.... *brrr!*)


-- 
:)
Veronica Karlsson
( e93...@sm.luth.se  http://www.ludd.luth.se/~vk/ )
( llizard's fanclub:  http://www.ludd.luth.se/~vk/llpages )

Dave Bird---St Hippo of Augustine wrote:

> In article <338...@garnet.fsu.edu>,
> Michael Naylor <mna...@garnet.fsu.edu> writes:
> >The Platonic, or
> >perfect, solids are those five shapes with every face a regular
> polygon,
> >and having the same number of edges meeting at each vertex...
> otherwise
> >known as "D & D dice".
>
> Omigawd. Remind me:  terahedron (three triangles meet at each vertex),
>
> cube (four squares meet at each vertex),  and...  Dodecahedron
> and Icosahedron, one is converse to the other i.e. got by drawing a
> dot
> for the centre of each face of the other, then that thing with 60
> vertices like the drawing on a football.  Hmm.  Yes, they might be
> a bit awkward to draw in ascii.
>
>                                             |~/           |~/
> ~~|;'^';-._.-;'^';-._.-;'^';-._.-;'^';-._.-;||';-._.-;'^';||_
> -;'^'0-|~~
> P |      Woof Woof, Glug Glug               ||____________||      0  |
> P
> O |   Who Drowned the Judge's Dog?          | . . . . . . . '----. 0 |
> O
> O |         answers on                  *---|_______________  @__o0  |
> O
> L |_<a href="news:alt.religion.scientology">________________|/_______|
> L
>  and<a href="http://www.xemu.demon.co.uk/clam/lynx/q0.html">

Here are a few ideas for the terahedron.  If someone can improve upon
them, please do so.
             ^
           /|\
          / | \
         /  |  \
     KCK '-.|.-'

             A
            *I=
           **I==
          ***I===
         ****I====
     KCK''_**I==_''
           - I -

            A
           /I\
          //I\\
         ///I\\\
     KCK '//I\\'
           'I'


               /A\
              /*I=\
             /**I==\
            /*^*I===\
           /*^**I====\
          /*^***I=^^==\
         /*^^^^^I^==^==\
        /*^^****I^======\
       /*^*^****I^=======\
      /*^**^****I^========\
       \***^****I^=======/
        \**^****I=^==^==/
   KCK   \*^****I==^^==/
          \^****I=====/
           \****I====/
            \***I===/
             \**I==/
              \*I=/
                V



                ^
               /A\
              //I\\
             ///I\\\
            ////I\\\\
           /////I\\\\\
          //////I\\\\\\
         ///////I\\\\\\\
        ////////I\\\\\\\\
       /////////I\\\\\\\\\
      //////////I\\\\\\\\\\
       '////////I\\\\\\\\'
   KCK   '//////I\\\\\\'
           '////I\\\\'
             '//I\\'
               'I'
--
Kevin

Veronica Karlsson wrote:
> 
> >
> > Anyways, yes, making these shapes in ASCII is a real challenge.  Any
> > takers?
> >
> 
> How about posting the URLs to some pictures... (I got the first three
> but then.... *brrr!*)
> 
> --
> :)
> Veronica Karlsson
> ( e93...@sm.luth.se  http://www.ludd.luth.se/~vk/ )
> ( llizard's fanclub:  http://www.ludd.luth.se/~vk/llpages )

Try here:
  http://www.cs.utk.edu/~plank/plank/pics/origami/kaleido_pics/pics.html

Greetz,
-- 
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