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Topic: Polyhedra Puzzle
Replies: 1   Last Post: Feb 23, 1993 6:13 AM

 Messages: [ Previous | Next ]
 David Wilson Posts: 3 Registered: 12/6/04
Polyhedra Puzzle
Posted: Oct 12, 1992 3:51 PM

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."

Date Subject Author
10/12/92 David Wilson
2/23/93 Vincent J. Matsko