TY - JOUR
T1 - The Numbers of Edges of 5-Polytopes with a Given Number of Vertices
AU - Kusunoki, Takuya
AU - Murai, Satoshi
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019/3/7
Y1 - 2019/3/7
N2 - A basic combinatorial invariant of a convex polytope P is its f-vector f(P) = (f, f 1 , ⋯ , f dim P - 1 ) , where f i is the number of i-dimensional faces of P. Steinitz characterized all possible f-vectors of 3-polytopes and Grünbaum characterized the pairs given by the first two entries of the f-vectors of 4-polytopes. In this paper, we characterize the pairs given by the first two entries of the f-vectors of 5-polytopes. The same result was also proved by Pineda-Villavicencio, Ugon and Yost independently.
AB - A basic combinatorial invariant of a convex polytope P is its f-vector f(P) = (f, f 1 , ⋯ , f dim P - 1 ) , where f i is the number of i-dimensional faces of P. Steinitz characterized all possible f-vectors of 3-polytopes and Grünbaum characterized the pairs given by the first two entries of the f-vectors of 4-polytopes. In this paper, we characterize the pairs given by the first two entries of the f-vectors of 5-polytopes. The same result was also proved by Pineda-Villavicencio, Ugon and Yost independently.
KW - Convex polytopes
KW - Face numbers
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U2 - 10.1007/s00026-019-00417-y
DO - 10.1007/s00026-019-00417-y
M3 - Article
AN - SCOPUS:85061285289
SN - 0218-0006
VL - 23
SP - 89
EP - 101
JO - Annals of Combinatorics
JF - Annals of Combinatorics
IS - 1
ER -