Zobrazeno 1 - 10
of 66
pro vyhledávání: '"Weiss, Asia Ivić"'
Autor:
Montero, Antonio, Weiss, Asia Ivić
Given any irreducible Coxeter group $C$ of hyperbolic type with non-linear diagram and rank at least $4$, whose maximal parabolic subgroups are finite, we construct an infinite family of locally spherical regular hypertopes of hyperbolic type whose C
Externí odkaz:
http://arxiv.org/abs/2102.01157
Autor:
Montero, Antonio, Weiss, Asia Ivić
We show that every non-degenerate regular polytope can be used to construct a thin, residually-connected, chamber-transitive incidence geometry, i.e. a regular hypertope, with a tail-triangle Coxeter diagram. We discuss several interesting examples d
Externí odkaz:
http://arxiv.org/abs/2001.11082
Autor:
Schulte, Egon, Weiss, Asia Ivić
Skeletal polyhedra and polygonal complexes are finite or infinite periodic structures in 3-space with interesting geometric, combinatorial, and algebraic properties. These structures can be viewed as finite or infinite periodic graphs (nets) equipped
Externí odkaz:
http://arxiv.org/abs/1610.02619
We study incidence geometries that are thin and residually connected. These geometries generalise abstract polytopes. In this generalised setting, guided by the ideas from the polytopes theory, we introduce the concept of chirality, a property of ord
Externí odkaz:
http://arxiv.org/abs/1604.03162
Up to isomorphism there are six fixed-point free crystallographic groups in Euclidean Space generated by twists (screw motions). In each case, an orientable 3-manifold is obtained as the quotient of E3 by such a group. The cubic tessellation of E3 in
Externí odkaz:
http://arxiv.org/abs/1505.00191
Guided by the ideas of chirality in the abstract polytope theory, the present paper aims to extend the concept to a more general setting of incidence geometries. The purpose of this paper is to explore the more general framework of thin residually co
Externí odkaz:
http://arxiv.org/abs/1411.6071
Every regular polytope has the remarkable property that it inherits all symmetries of each of its facets. This property distinguishes a natural class of polytopes which are called hereditary. Regular polytopes are by definition hereditary, but the ot
Externí odkaz:
http://arxiv.org/abs/1206.1647
Unlike the situation in the classical theory of convex polytopes, there is a wealth of semi-regular abstract polytopes, including interesting examples exhibiting some unexpected phenomena. We prove that even an equifacetted semi-regular abstract poly
Externí odkaz:
http://arxiv.org/abs/1109.2280
Autor:
Schulte, Egon, Weiss, Asia Ivic
The paper gives a collection of open problems on abstract polytopes that were either presented at the Polytopes Day in Calgary or motivated by discussions at the preceding Workshop on Convex and Abstract Polytopes at the Banff International Research
Externí odkaz:
http://arxiv.org/abs/math/0608397
Every finite, self-dual, regular (or chiral) 4-polytope of type {3,q,3} has a trivalent 3-transitive (or 2-transitive) medial layer graph. Here, by dropping self-duality, we obtain a construction for semisymmetric trivalent graphs (which are edge- bu
Externí odkaz:
http://arxiv.org/abs/math/0606469