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Topic: Polyhedra Puzzle
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David Wilson

Posts: 3
Registered: 12/6/04
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

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 (

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