# Negatively curved graphite and triply periodic minimal surfaces

@article{Terrones1994NegativelyCG, title={Negatively curved graphite and triply periodic minimal surfaces}, author={Humberto Terrones and Alan Lindsay Mackay}, journal={Journal of Mathematical Chemistry}, year={1994}, volume={15}, pages={183-195} }

The Weierstrass representation has been used to construct negatively curved graphite in which atoms rest no a perfect triply periodic minimal surface. By applying the Bonnet transformation on a patch of the D surface decorated with graphite we have been able to construct the Gyroid and P minimal surfaces. Curvatures, densities and lattice parameters have been calculated. It has been found that the maximum Gaussian curvature for our negatively curved structures is less in magnitude than the…

## 17 Citations

Curved graphite and its mathematical transformations

- Mathematics
- 1994

Mathematical transformations for graphite with positive, negative and zero Gaussian curvatures are presented. When the Gaussian curvatureK is zero, we analyse a bending transformation from a planar…

Classification of hypothetical doubly and triply periodic porous graphitic structures by tilings of neck-like units

- Mathematics
- 2010

In this study, we extend the concept of constructing high-genus fullerenes with neck-like structures to the classification of a wide family of doubly periodic graphitic structures. The neck…

Construction of Negatively Curved Cubic Carbon Crystals via Standard Realizations

- Mathematics
- 2016

In Tagami et al. (Carbon 76:266–274, 2014), we constructed physically stable sp2 negatively curved cubic carbon structures which reticulate a Schwarz P-like surface. The method for constructing such…

The topology of fullerenes

- MathematicsWiley interdisciplinary reviews. Computational molecular science
- 2015

A general overview of recent topological and graph theoretical developments in fullerene research over the past two decades is presented, describing both solved and open problems.

The topology of fullerenes The topology of fullerenes Kekulé Structures and Perfect Matchings,

- Mathematics
- 2014

Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical…

Structural, energetic, and electronic properties of gyroidal graphene nanostructures

- Materials Science
- 2016

Systematics of High-Genus Fullerenes

- MathematicsJ. Chem. Inf. Model.
- 2009

A systematic way to classify a family of high-genus fullerenes (HGFs) by decomposing them into two types of necklike structures, which are the negatively curved parts of parent toroidal carbon nanotubes is presented.

An alternative structure for C576

- Physics
- 1999

Abstract Carbon nanotubes with rollup vector indices equal, i. e., (n, n) nanotubes, are calculated to be metallic electrical conductors. Several years ago, a toroidal fullerene structure, C576, was…

Curvature matching and strain relief in bucky-tori: usage of sp3-hybridization and nonhexagonal rings.

- EngineeringJournal of molecular graphics & modelling
- 2001

## References

SHOWING 1-10 OF 23 REFERENCES

Curved graphite and its mathematical transformations

- Mathematics
- 1994

Mathematical transformations for graphite with positive, negative and zero Gaussian curvatures are presented. When the Gaussian curvatureK is zero, we analyse a bending transformation from a planar…

Negatively curved graphitic sheet model of amorphous carbon.

- Materials SciencePhysical review letters
- 1992

Like their periodic counterparts, the random structures are found to be exceptionally stable and match closely those of films of amorphous carbon grown on NaCl substrates from sublimated graphite.

The topology and geometry of infinite periodic surfaces

- Mathematics
- 1989

The use of space group stereohedra derived by Bashkirov as free boundaries result in a multiplicity of intersection-free (as well as self-intersecting) translationally periodic minimal surfaces of…

Parametrization of triply periodic minimal surfaces. II. Regular class solutions

- Mathematics
- 1992

A derivation is given of the set of triply periodic minimal surfaces of monoclinic symmetry and higher that fall within the regular class (including those containing self-intersections). The Gauss…

Energetics of negatively curved graphitic carbon

- ChemistryNature
- 1992

BY analogy with the positively curved carbon networks that comprise the fullerenes1–3, it has been suggested4 that negative curvature might be possible in graphitic carbon sheets, giving rise to…

Parametrization of triply periodic minimal surfaces. I : Mathematical basis of the construction algorithm for the regular class

- Mathematics
- 1992

An explicit parametrization algorithm is reported for the simplest class of triply periodic minimal surfaces (the `regular' class) for which the Weierstrass function specifying the complex plane…

A construction algorithm for minimal surfaces

- Mathematics
- 1987

Infinite periodic minimal surfaces are constructed from complex functions, which are simply related to the orientation of flat points on the surface. Two tetragonal familities of surfaces are…

C60: Buckminsterfullerene

- PhysicsNature
- 1985

During experiments aimed at understanding the mechanisms by which long-chain carbon molecules are formed in interstellar space and circumstellar shells1, graphite has been vaporized by laser…

Differential geometry of crystal structure descriptions, relationships and phase transformation

- Mathematics
- 1985

The mathematical background for the differential geometry of periodic minimal surfaces is given and used to describe and construct the gyroid surface (space group M{i2). A differential geometric…