Related papers: Sizes of Pentagonal Clusters in Fullerenes
For each $d>0$, we find all the smallest fullerenes for which the least distance between two pentagons is $d$. We also show that for each $d$ there is an $h_d$ such that fullerenes with pentagons at least distance $d$ apart and any number…
Fullerenes are hollow carbon molecules where each atom is connected to exactly three other atoms, arranged in pentagonal and hexagonal rings. Mathematically, they can be combinatorially modeled as planar, 3-regular graphs with facets…
We describe a new construction algorithm for the recursive generation of all non-isomorphic IPR fullerenes. Unlike previous algorithms, the new algorithm stays entirely within the class of IPR fullerenes, that is: every IPR fullerene is…
We have performed molecular dynamics simulations on the formation of mixed molecular clusters of buckminsterfullerene and coronene, $(\mathrm{C}_{24}\mathrm{H}_{12})_n(\mathrm{C}_{60})_{N-n}$. We report on our findings on the structures and…
Fullerenes are an allotrope of carbon having hollow, cage-like structure. Atoms in the molecule are arranged in pentagonal and hexagonal rings, such that each atom is connected to three other atoms. Simple polyhedra having only pentagonal…
In interstellar environment, fullerene species readily react with large molecules (e.g., PAHs and their derivatives) in the gas phase, which may be the formation route of carbon dust grains in space. In this work, the gas-phase ion-molecule…
There has long been a discrepancy between the size distributions of Ar$_n^+$ clusters measured by different groups regarding whether or not magic numbers appear at sizes corresponding to the closure of icosahedral (sub-)shells. We show that…
We study the well-known problem of combinatorial classification of fullerenes. By a (mathematical) fullerene we mean a convex simple three dimensional polytope with all facets pentagons and hexagons. We analyse approaches of construction of…
We explore some generalizations of fullerenes F_v (simple polyhedra with v vertices and only 5- and 6-gonal faces) seen as (d-1)-dimensional simple manifolds (preferably, spherical or polytopal) with only 5- and 6-gonal 2-faces. First,…
A fullerene graph can be embedded in a piecewise linear 2-manifold with each non-hexagonal carbon ring corresponding to a cone vertex. Adjacent two or three such vertices can be combined as a cluster cut out from a parent cone round a…
A pentagonal geometry PENT($k$, $r$) is a partial linear space, where every line, or block, is incident with $k$ points, every point is incident with $r$ lines, and for each point $x$, there is a line incident with precisely those points…
A fullerene graph $F$ is a planar cubic graph with exactly 12 pentagonal faces and other hexagonal faces. A set $\mathcal{H}$ of disjoint hexagons of $F$ is called a resonant pattern (or sextet pattern) if $F$ has a perfect matching $M$…
We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes -- fullgen -- and the first program since…
So far, no boron fullerenes were synthesized: more compact sp3-bonded clusters are energetically preferred. To circumvent this, metallic clusters have been suggested by Pochet et al. [Phys. Rev. B 83, 081403(R) (2011)] as "seeds" for a…
Steffen's polyhedron was believed to have the least number of vertices among polyhedra that can flex without self-intersections. Maksimov clarified that the pentagonal bipyramid with one face subdivided into three is the only polyhedron…
A fullerene graph is a cubic 3-connected plane graph with (exactly 12) pentagonal faces and hexagonal faces. Let $F_n$ be a fullerene graph with $n$ vertices. A set $\mathcal H$ of mutually disjoint hexagons of $F_n$ is a sextet pattern if…
A simple pair potential, which equilibrium pair separation can be varied under a fixed interaction range, has been proposed. The new potential can make both face-centered-cubic(fcc) and body-centered-cubic(bcc) structure stable by simply…
The effect of the finite size of an array of scatterers on the position of the resonance poles of the scattered amplitudes is studied. This effect must be studied because in reality, an infinite array cannot be realized. In particular, it…
We construct, for any positive integer n, a family of n congruent convex polyhedra in R^3, such that every pair intersects in a common facet. Previously, the largest such family contained only eight polytopes. Our polyhedra are Voronoi…
The main objective of this paper is to study the size of a typical cluster of bond percolation on each of the five Platonic solids: the tetrahedron, the cube, the octahedron, the dodecahedron and the icosahedron. Looking at the clusters…