TY - JOUR
T1 - Three theorems, with computer-aided proofs, on three-dimensional faces and quotients of polytopes
AU - Meisinger, G.
AU - Kleinschmidt, P.
AU - Kalai, G.
PY - 2000
Y1 - 2000
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.
UR - http://www.scopus.com/inward/record.url?scp=0034371208&partnerID=8YFLogxK
U2 - 10.1007/s004540010045
DO - 10.1007/s004540010045
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AN - SCOPUS:0034371208
SN - 0179-5376
VL - 24
SP - 413
EP - 420
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
IS - 2-3
ER -