>   Specially if all the triangles are inside the same mesh.
>   There isn't really big rendering speed difference between 100000 and 200000
> triangles when they are inside the same mesh (a couple of % perhaps).

Does this mean two copies of twenty-four different meshes will render
faster than forty-eight intersections of planes?  Or is the number of
polyhedra I will use too small to matter?  I'll go for the meshes.  It
would be easier to figure out where the vertexes of the triangles are by
looking at pictures or by truncating or stellating more basic polyhedra
than to figure out how the planes need to be rotated and translated.  I
will  define them so that they will rest on plane { y,0 }.  I'll make
the cube the Platonic solid with the most surface area in contact with
the plane.  The triangles and pentagons of the other Platonic solids
will be inscribed into the square used for the cube.  Then I will make
other shapes by truncating and stellating these solids.  The truncated
ones will be smaller and the stellated ones will be larger.  I will try
to figure out how big the polyhedra game board will need to be to
contain all of the polyhedra by finding the area of the bounding boxes
of the largest polyhedra.
Brendan

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