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Polyhedra Puzzle
Posted:
Oct 12, 1992 3:51 PM
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Let P and Q be two polyhedra in Euclidean 3-space, with the following
properties:
P and Q have the same set of polygon faces. For instance, P
and Q might each have, say, 6 square and 8 equilateral
triangular faces, of the same size.
P and Q are distinct up to translation, rotation, and reflection.
What, that, are the smallest number of faces P may have under each
of the following conditions:
1. P and Q have distinct volume.
2. P and Q have distinct volume and regular polygon faces.
3. P and Q have equal volume.
4. P and Q have equal volume and regular polygon faces.
--
David W. Wilson (wilson@neptune.ctron.com)
Disclaimer: "Truth is just truth...You can't have opinions about truth."
- Peter Schikele, introduction to P.D.Q. Bach's oratorio "The Seasonings."
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