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A Computer Generation of Polytopes that are Sections of the 5-Cube

C. Caiseda
L. González
Journal / Anthology

Congressus Numerantium
Year: 1993
Volume: 93
Page range: 159-176

An interesting application of cut-complexes is to generate convex polytopes that are sections of the hypercube. Through the implementation of three graph transformations in Mathematica, all distinct convex polytopes which are sections of the 5-cube can be generated. The transformations on the well-known 2-faces of the polytopal section P-H intersect c5 are also studied. Three Corollaries, following from Theorem 1 and Theorem 2 are introduced to justify such transformations. Finally some computational results are presented.

*Mathematics > Geometry > Solid Geometry