Infinite Families of Hypertopes from Centrally Symmetric Polytopes
نویسندگان
چکیده
We construct infinite families of abstract regular polytopes Schläfli type $\{4,p_1,\ldots,p_{n-1}\}$ from extensions centrally symmetric spherical $n$-polytopes. In addition, by applying the halving operation, we obtain both locally and toroidal hypertopes $\left\{\genfrac{}{}{0pt}{}{p_1}{p_1},\ldots,p_{n-1}\right\}$.
منابع مشابه
Centrally symmetric polytopes with many faces
We present explicit constructions of centrally symmetric polytopes with many faces: (1) we construct a d-dimensional centrally symmetric polytope P with about 3d/4 ≈ (1.316)d vertices such that every pair of non-antipodal vertices of P spans an edge of P , (2) for an integer k ≥ 2, we construct a d-dimensional centrally symmetric polytope P of an arbitrarily high dimension d and with an arbitra...
متن کاملFace Numbers of Centrally Symmetric Polytopes Produced from Split Graphs
We analyze a remarkable class of centrally symmetric polytopes, the Hansen polytopes of split graphs. We confirm Kalai’s 3d conjecture for such polytopes (they all have at least 3d nonempty faces) and show that the Hanner polytopes among them (which have exactly 3d nonempty faces) correspond to threshold graphs. Our study produces a new family of Hansen polytopes that have only 3d + 16 nonempty...
متن کاملOn Kalai's Conjectures Concerning Centrally Symmetric Polytopes
In 1989 Kalai stated the three conjectures A, B, C of increasing strength concerning face numbers of centrally symmetric convex polytopes. The weakest conjecture,A, became known as the “3-conjecture”. It is well-known that the three conjectures hold in dimensions d ≤ 3. We show that in dimension 4 only conjectures A and B are valid, while conjecture C fails. Furthermore, we show that both conje...
متن کاملOn the number of faces of centrally-symmetric simplicial polytopes
I. Bfirfiny and L. Lovfisz [Acta Math. Acad. Sci. Hung. 40, 323-329 (1982)] showed that a d-dimensional centrally-symmetric simplicial polytope ~ has at least 2 d facets, and conjectured a lower bound for the number f~ of i-dimensional faces o f ~ in terms ofd and the number f0 = 2n of d vertices. Define integers ho . . . . . he by Z f~-1(x 1) d-' = ~ hi xd-'. A. Bj6rner conjectured (uni=O i=O ...
متن کاملHigh-Dimensional Centrally Symmetric Polytopes with Neighborliness Proportional to Dimension
Let A be a d by n matrix, d < n. Let C be the regular cross polytope (octahedron) in R. It has recently been shown that properties of the centrosymmetric polytope P = AC are of interest for finding sparse solutions to the underdetermined system of equations y = Ax; [9]. In particular, it is valuable to know that P is centrally k-neighborly. We study the face numbers of randomly-projected cross-...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Journal of Combinatorics
سال: 2023
ISSN: ['1077-8926', '1097-1440']
DOI: https://doi.org/10.37236/10392