Intersecting All Edges of Centrally Symmetric Polyhedra by Planes.
WASHINGTON UNIV SEATTLE DEPT OF MATHEMATICS
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Motivated by information-theoretic problems P. E. ONeil has recently investigated the question how many hyperplanes are needed to cut all edges of an n-cube. A similar problem is investigated in this report, restricting the dimension but generalizing the class of polytopes. It is established that if P is a centrally symmetric convex polyhedron in 3-space then it is impossible to intersect all the edges of P by any pair of planes that miss the vertices of P. However, there exist convex 3-polytopes without a center of symmetry, as well as centrally symmetric tessellations of the 2-sphere, in which all edges may be intersected by a suitable pair of planes. Author
- Theoretical Mathematics