Zobrazeno 1 - 10
of 15
pro vyhledávání: '"Rasskin, Ivan"'
In this paper, we establish a connection between Apollonian packings and knot theory. We introduce new representations of links realized in the tangency graph of the regular crystallographic sphere packings. Particularly, we prove that any algebraic
Externí odkaz:
http://arxiv.org/abs/2301.03089
Publikováno v:
In European Journal of Combinatorics December 2024 122
Autor:
Rasskin, Iván
Publikováno v:
Geometriae Dedicata 218, 105 (2024)
In this paper, we explore the geometry and the arithmetic of a family of polytopal sphere packings induced by regular polytopes in any dimension. We prove that every integral polytope is crystallographic, and we show that there are 11 crystallographi
Externí odkaz:
http://arxiv.org/abs/2109.00655
We present a generalization of Descartes' theorem for the family of polytopal sphere packings arising from uniform polytopes. The corresponding quadratic equation is expressed in terms of geometric invariants of uniform polytopes which are closely co
Externí odkaz:
http://arxiv.org/abs/2107.09432
In this paper, we investigate representations of links that are either centrally symmetric in $\mathbb{R}^3$ or antipodally symmetric in $\mathbb{S}^3$. By using the notions of antipodally self-dual and antipodally symmetric maps, introduced and stud
Externí odkaz:
http://arxiv.org/abs/2106.05376
The ball number of a link $L$, denoted by $ball(L)$, is the minimum number of solid balls (not necessarily of the same size) needed to realize a necklace representing $L$. In this paper, we show that $ball(L)\leq 5 cr(L)$ where $cr(L)$ denotes the cr
Externí odkaz:
http://arxiv.org/abs/2010.00580
A self-dual map $G$ is said to be \emph{antipodally self-dual} if the dual map $G^*$ is antipodal embedded in $\mathbb{S}^2$ with respect to $G$. In this paper, we investigate necessary and/or sufficient conditions for a map to be antipodally self-du
Externí odkaz:
http://arxiv.org/abs/2008.12853
Akademický článek
Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
K zobrazení výsledku je třeba se přihlásit.
K zobrazení výsledku je třeba se přihlásit.
Akademický článek
Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
K zobrazení výsledku je třeba se přihlásit.
K zobrazení výsledku je třeba se přihlásit.
Publikováno v:
In European Journal of Combinatorics August 2021 96