Abstract.
We prove that there is a finite list of 3-polytopes so that every rational d -polytope, d ≥ 9 , contains a three-dimensional face in the list. A similar result where ``faces'' are replaced by ``quotients'' is proved already for (general) 5-polytopes. We also prove that every d -polytope, d ≥ 9 , contains a three-dimensional quotient which is a simplex.
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Meisinger, G., Kleinschmidt, P. & Kalai, G. Three Theorems, with Computer-Aided Proofs, on Three-Dimensional Faces and Quotients of Polytopes. Discrete Comput Geom 24, 413–420 (2000). https://doi.org/10.1007/s004540010045
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DOI: https://doi.org/10.1007/s004540010045