A fullerene graph is a 3 regular planar simple finite graph with pentagon or hexagon faces. In these graphs the number of pentagon faces is 12. Therefore, any fullerene graph can be characterized by number of its hexagon faces. In this note, for any h > 1, we will construct a fullerene graph with h hexagon faces. Then, using the leapfrogging process we will construct stable fullerenes with 20 +...

We calculate the Riemann-Roch number of some of the pentagon spaces defined in [Kl, KM, HK1]. Using this, we show that while the regular pentagon space is diffeomorphic to a toric variety, even symplectomorphic to one under arbitrarily small perturbations of its symplectic structure, it does not admit a symplectic circle action. In particular, within the cohomology classes of symplectic structu...

Sustainable design and constructability are two keys for efficient design and construction that are often addressed separately from each other in projects. This paper examines the integration of these two initiatives on the Pentagon renovation. The examination exposes a synergistic relationship between sustainable design and constructability. This relationship strives to efficiently utilize res...

by employing the theoretical method based on tight-binding, we study electronic band structure of single-wall carbon nanotube (cnt) superlattices, which the system is the made of the junction between the zigzag and armchair carbon nanotubes. exactly at the place of connection, it is appeared the pentagon–heptagon pairs as topological defect in carbon hexagonal network. the calculations are base...

By employing the theoretical method based on tight-binding, we study electronic band structure of single-wall carbon nanotube (CNT) superlattices, which the system is the made of the junction between the zigzag and armchair carbon nanotubes. Exactly at the place of connection, it is appeared the pentagon–heptagon pairs as topological defect in carbon hexagonal network. The calculations are base...

(19 June 2012) We introduce the concept of a pentagonal geometry as a generalisation of the pentagon and the Desargues configuration, in the same vein that the generalised polygons share the fundamental properties of ordinary polygons. In short, a pentagonal geometry is a regular partial linear space in which for all points x, the points not collinear with the point x, form a line. We compute b...