Three theorems, with computer-aided proofs, on three-dimensional faces and quotients of polytopes

G. Meisinger; P. Kleinschmidt; G. Kalai

doi:10.1007/s004540010045

Three theorems, with computer-aided proofs, on three-dimensional faces and quotients of polytopes

G. Meisinger^*
, P. Kleinschmidt
, G. Kalai

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Pages (from-to)	413-420
Number of pages	8
Journal	Discrete and Computational Geometry
Volume	24
Issue number	2-3
DOIs	https://doi.org/10.1007/s004540010045
State	Published - 2000

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N2 - 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.

AB - 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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JO - Discrete and Computational Geometry

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IS - 2-3

ER -

Three theorems, with computer-aided proofs, on three-dimensional faces and quotients of polytopes

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