Related papers: Highly symmetric hypertopes

Chirality, or handedness, is a topic that is common in biology and chemistry, yet is rarely discussed in physics courses. We provide a way of introducing the topic in classical physics, and demonstrate the merits of its inclusion - such as…

Symmetric edge polytopes are a recent and well-studied family of centrally symmetric polytopes arising from graphs. In this paper, we introduce a generalization of this family to arbitrary simplicial complexes. We show how topological…

In condensed matter physics, a broad spectrum of physical characteristics, such as chirality, axiality, and polarity, arises as a direct consequence of the underlying symmetry of the system. We here theoretically investigate the effective…

For Cartan geometries admitting automorphisms with isotropies satisfying a particular, loosely dynamical property on their model geometries, we demonstrate the existence of an open subset of the geometry with trivial holonomy. This…

We analyze the "higher rank" gauge theories, that capture some of the phenomenology of the Fracton order. It is shown that these theories lose gauge invariance when arbitrarily weak and smooth curvature is introduced. We propose a…

The aim of this paper is to use the framework of incidence geometry to develop a theory that permits to model both the inner and outer automorphisms of a group G simultaneously. More precisely, to any group G, we attempt to associate an…

In this paper we prove geometric residue theorems for bundle maps over a compact manifold. The theory developed associates residues to the singularity submanifolds of the map for any invariant polynomial. The theory is then applied to a…

An object is chiral when its symmetry group contains no indirect isometry. It can be difficult to classify isometries as direct or indirect, except in the Euclidean case. We classify them with the help of outer semidirect products of…

Random shapes arise naturally in many contexts. The topological and geometric structure of such objects is interesting for its own sake, and also for applications. In physics, for example, such objects arise naturally in quantum gravity, in…

Chirality plays a crucial role in determining the structure of many systems in nature. Twisted or helical aggregates as a consequence of self-assembly can be seen in many biological and synthetic materials. Despite extensive theoretical and…

An abstract $n$-polytope $\mathcal{P}$ is a partially-ordered set which captures important properties of a geometric polytope, for any dimension $n$. For even $n \ge 2$, the incidences between elements in the middle two layers of the Hasse…

Chirality is of primary importance in many areas of chemistry and has been extensively investigated since its discovery. We introduce here the description of central chirality for tetrahedral molecules using a geometrical approach based on…

We investigate the geometry of holomorphic curves and complex surfaces from the perspective of singularity theory. We show that, with a suitable choice of a complex bilinear symmetric form, the families of functions and mappings that…

Quasirandomness is a general mathematical concept meant to encapsulate several characteristics usually satisfied by random combinatorial objects, and which we regard as describing when a given object 'looks random'. In this survey we…

Abstract polytopes are combinatorial objects that generalise geometric objects such as convex polytopes, maps on surfaces and tilings of the space. Chiral polytopes are those abstract polytopes that admit full combinatorial rotational…

We reveal a previously unknown continuous symmetry and conservation law in the equations of linear isotropic elasticity, which describe the chirality of elastic waves. We show that the integral chirality is determined by the population…

We show that chiral symmetry can be broken spontaneously in one-component systems with isotropic interactions, i.e. many-particle systems having maximal a priori symmetry. This is achieved by designing isotropic potentials that lead to…

Chirality is a universal feature in nature, as observed in fermion interactions and DNA helicity. Much attention has been given to chiral interactions of light, not only regarding its physical interpretation but also focusing on intriguing…

We investigate the relationship between finite groups and incidence geometries through their automorphism structures. Building upon classical results on the realizability of groups as automorphism groups of graphs, we develop a general…

We develop a theory of chirality and racemization on isotopy classes of finite loops, formulated intrinsically within the loop isotopy groupoid understood in the categorical sense. Motivated by earlier work on quasigroups…