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## Publications

Publications (26)

This paper covers aspects of quantifying the symmetry of two- and three-dimensional elastic bar-and-joint structures. The concept of symmetry as a quantitative property instead of a binary question of 'yes' or 'no' is widely accepted and thoroughly investigated, for example, in molecular physics but also in engineering sciences, mainly in chemical...

This paper covers aspects of establishing a relationship between the highest-order rotation-invariant moments of inertia and the order of symmetry of Platonic polyhedra. Moments of inertia about arbitrary, but centroidal axes are considered. After an introductory part which summarizes the possible applications of higher-order moments of area and in...

There is increasing interest in two-dimensional and quasi-two-dimensional materials and metamaterials for applications in chemistry, physics and engineering. Some of these applications are driven by the possible auxetic properties of such materials. Auxetic frameworks expand along one direction when subjected to a perpendicular stretching force. An...

The monostatic property of convex polyhedra (i.e. the property of having just one stable or unstable static equilibrium point) has been in the focus of research ever since Conway and Guy (1969) published the proof of the existence of the first such object, followed by the constructions of Bezdek (2011) and Reshetov (2014). These examples establish...

We show an explicit construction in 3 dimensions for a convex, mono-monostatic polyhedron with 21 vertices and 21 faces. This polyhedron is a homogeneous 0-skeleton, with equal masses located at each vertex. This construction serves as an upper bound for the minimal number of faces and vertices of mono-monostatic polyhedra, interpreted as homogeneo...

The monostatic property of convex polyhedra (i.e. the property of having just one stable or unstable static equilibrium point) has been in the focus of research ever since Conway and Guy published the proof of the existence of the first such object, followed by the constructions of Bezdek and Reshetov. These examples establish $F\leq 14, V\leq 18$...

We define the mechanical complexity $C(P)$ of a convex polyhedron $P,$ interpreted as a homogeneous solid, as the difference between the total number of its faces, edges and vertices and the number of its static equilibria, and the mechanical complexity $C(S,U)$ of primary equilibrium classes $(S,U)^E$ with $S$ stable and $U$ unstable equilibria as...

Some closed polyhedral surfaces can be completely covered by two-way, twofold (rectangular) weaving of strands of constant width. In this paper, a construction for producing all possible geometries for such weavable cuboids is proposed: a theorem on spherical octahedra is proven first that all further theory is based on. The construction method of...

Strings on the surface of gift boxes can be modelled as a special kind of cable-and-joint structure. This paper deals with systems composed of idealised (frictionless) closed loops of strings that provide stable binding to the underlying convex polyhedron (‘package’). Optima are searched in both the sense of topology and geometry in finding minimal...

This paper deals with two- and threefold weavings on Platonic polyhedral surfaces. Depending on the skewness of the weaving pattern with respect to the edges of the polyhedra, different numbers of closed strands are necessary in a complete weaving. The problem is present in basketry but can be addressed from the aspect of pure geometry (geodesics),...

An infinite series of twofold, two-way weavings of the cube, corresponding to ‘wrappings’, or double covers of the cube, i described with the aid of the two-parameter Goldberg–Coxeter construction. The strands of all such wrappings correspond t the central circuits (CCs) of octahedrites (four-regular polyhedral graphs with square and triangular fac...

This paper traces a way of generalization of the classical truss theory: in addition to the kinematic constraint expressing the distance between two nodes connected by a bar element, other similar constraints involving three and four nodes are introduced. Derived from energy principles, a general tangent stiffness formulation is given. Possible mec...

This paper discusses a 2D truss formulation with spherical angular variables for bar-and-joint assemblies existing in 3D on the surface of a sphere. Based on the principle of potential energy, coupled problems of equilibrium and compatibility, as well as of stiffness and prestress stability are investigated. Finally, the results are illustrated by...

Double-link expandohedra are introduced: each is constructed from a parent polyhedron by replacing all faces with rigid plates, adjacent plates being connected by a pair of spherically jointed bars. Powerful symmetry techniques are developed for mobility analysis of general double-link expandohedra, and when combined with numerical calculation and...

This paper discusses the possibility of detecting mechanisms with second-order stiffness (resistance to the excitation of an infinitesimal mechanism) imposed by self-stresses in highly symmetric structures. Coupled application of symmetry adapted first-order matrix analysis and a second-order stiffness analysis is performed, then the symmetry adapt...

A class of expandable polyhedral structures, the expandohedra, consisting of prismatic faces linked along edges by hinged plates, provides a model for the swelling of viruses. The finite breathing mode of the expandohedra, apparent in the model, and from geometric arguments, is not, however, detected by elementary counting techniques. Symmetry exte...

SUMMARY Some bar structures have already been invented that have a closed circular shape and are foldable along their perimeter. These mechanisms usually belong to one of the two following basic categories: either they contain exclusively hinges and pivots ( scissor-like hinges) but can move only along a plane, or they are able to move along other...

The Cowpea Chlorotic Mottle Virus (CCMV) is able to vary its diameter due to pH change such that the assembly retains its original icosahedral symmetry during this swelling motion . In the first step, a is set up, then are analysed by ; finally, of swelling is investigated. ' ' mechanical ball-jointed model mobility and self-stresses

Many viruses have an outer protein coat with the structure of a truncated icosahedron, and can expand following changes to the environment around the virus. The protein coat consists of chemically identical protein subunits that form pentagonal or hexagonal capsomeres; these move apart during expansion, opening interstices and allowing access to th...

A mechanism found in biology: the swelling motion of some specific virus structures is simulated by a ball-jointed mechanical model. Symmetry arguments are used to qualify its mobility properties and an analytical description is given for the pathway of this swelling motion that reveals the existence of kinematic bifurcation.

A mérnöki gyakorlathoz kapcsolódó mechanikai problémák sok esetben vezetnek nemlineáris numerikus feladatra. Ilyen feladatot jelent többek között a szerkezetek stabilitásvizsgálata, a nagy elmozdulásokkal kapcsolatos vizsgálatok, illetve geodéziai eredetű számítási problémák is. Kutatásaink során megmutattuk, hogy rugalmas szerkezetek stabilitásána...

Numerikus megoldásokat állítottunk elő a körpárok és körhármasok gömbön való legsűrűbb elhelyezésének problémájára, és szimmetria alapú vizsgálatokat végeztünk a gömbi körelhelyezés gráfjának Danzer-féle merevségére vonatkozóan. Egy általunk bevezetett gömbölyűségi kritérium alapján optimális, gömböt közelítő poliédereket konstruáltunk. A szakrális...