bbadger@x102c.harris-atd.com (Badger BA 64810) (01/08/90)
I'd like to know an effective means of constructing and displaying
polyhedra build up from parts. There are two cases I'm considering:
1) Polyhedra built from rigid polygons. E.g., a cube from six squares,
an icosahedron from 20 equilateral triangles.
2) Polyhedra build from line segments. E.g., a cube from twelve ``sticks''.
I already know the specific answers to the Platonic solids, what I'm
interested in are approaches to a ``construction set''. In
particular, I'd like to know when there are multiple solutions to any
particular connection graph. (Note that a mirror reflection is always
a solution. An icosahedron can have many points ``dented in'' and
still work.) Only the sizes of the pieces and their connection graph
are known at the start, the dihedral angles all must be computed.
Specialized solutions (e.g., triangles only) are acceptable.
Whenever I've tried to figure this myself, I get bogged down in simultaneous
quadratic or trigonometric equations. Any tips, programs or references
appreciated.
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Bernard A. Badger Jr. 407/984-6385 |``Get a LIFE!'' -- J.H. Conway
Harris GISD, Melbourne, FL 32902 |Buddy, can you paradigm?
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