Fullerenes and coordination polyhedra versus half-cube embeddings

  title={Fullerenes and coordination polyhedra versus half-cube embeddings},
  author={Antoine Deza and Michel Deza and Viatcheslav P. Grishukhin},
  journal={Discret. Math.},

Version of Zones and Zigzag Structure in Icosahedral Fullerenes and Icosadeltahedra

A full analysis of the zone and zigzag structure is made for icosahedral centrosymmetric fullerenes and their duals, which provides hypercube embeddings of these classes of polyhedra which preserve all graph distances up to a limit that depends on the vertex count.

On octahedral fulleroids

Local Combinatorial Characterization of Fullerenes

We present a general method which enables a possible classification of fullerenes by means of local topological invariants. In this study fullerenes are considered as bifaced simple (trivalent)

The Chirality of Icosahedral Fullerenes: a Comparison of the Tripling (leapfrog), Quadrupling (chamfering), and Septupling (capra) Transformations

Fullerene polyhedra of icosahedral symmetry have the midpoints of their 12 pentagonal faces at the vertices of a macroicosahedron and can be characterized by the patterns of their hexagonal faces on

Extended Superspheres for Shape Approximation of Near Polyhedral Nanoparticles and a Measure of the Degree of Polyhedrality

  • S. Onaka
  • Materials Science
  • 2016
Algebraic formulas of extended superspheres that can express intermediate shapes between spheres and various polyhedra have been presented to consider near polyhedral shapes ofCrystalline nanoparticles or nanoprecipitates with a cubic structure.

On cyclic edge-connectivity of fullerenes

From the Cube to the Dyck and Klein Tessellations: Implications for the Structures of Zeolite-like Carbon and Boron Nitride Allotropes

Geometrical transformations can be described which have the effect of multiplying the numbers of vertices in a trivalent polyhedron by three, four, or seven. Tripling the cube by the so-called

The Roundest Polyhedra with Symmetry Constraints

A new numerical optimization method has been applied to optimize polyhedra to best approximate a sphere if tetrahedral, octahedral, or icosahedral symmetry constraints are applied.



Geodesic domes and fullerenes

  • T. Tarnai
  • Mathematics
    Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences
  • 1993
The structural form of geodesic domes, composed of pentagons and hexagons, played an important role in understanding the structure of carbon clusters. In this paper an analogy between geodesic domes

Systematics of bonding in non-icosahedral carbon clusters

General formulas are presented for the vertex numbers, ν, of pentagon+hexagon polyhedra of icosahedral, tetrahedral or dihedral symmetries. Criteria for uniqueness of representation, isomer counts

Topological aspects of chemically significant polyhedra

This paper considers both static and dynamic properties of chemically significant polyhedra. Static properties of polyhedra consider relationships between the numbers and degrees/sizes of polyhedral

Polyoxometalates: A class of compounds with remarkable topology

Structures of polyoxometalates frequently are discovered to be based upon regular convex polyhedra, including the Platonic and Archimedean solids. A topological approach involving barycentric

Leapfrog transformations and polyhedra of Clar type

The so-called leapfrog transformation that was first introduced for fullerenes (trivalent polyhedra with 12 pentagonal faces and all other faces hexagonal) is generalised to general polyhedra and

Magic numbers in polygonal and polyhedral clusters

Certain values for the nuclearity of clusters tend to occur more frequently than others. This paper gives a mathematical derivation of the preferred values of nuclearity (the “magic numbers”)

Theory on the structure and stability of coated vesicles.

  • I. Katsura
  • Chemistry
    Journal of theoretical biology
  • 1983

A Constructive Enumeration of Fullerenes

In this paper, a fast and complete method to enumerate fullerene structures is given. It is based on a top-down approach, and it is fast enough to generate, for example, all 1812 isomers ofC60in less

Closo boron hydrides with 13 to 24 boron atoms

Structures are proposed for hypothetical closo boron hydrides ranging in size from B/sub 13/H/sub 13//sup 2 -/ to B/sub 24/H/sub 24//sup 2 -/. The proposed B/sub n/H/sub n//sup 2 -/ structures are