Re: 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".

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   _/\_

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