In this paper, we give a complete description of the farthest point map, as defined on regular octahedron with its intrinsic flat cone metric. As consequence show that every well-defined orbit map converges to 1-skeleton barycentric subdivision triangulation.

Coverage and connectivity issues of three-dimensional (3D) networks are addressed in [2], but that work assumes that a node can be placed at any arbitrary location. In this work, we drop that assumption and rather assume that nodes are uniformly and densely deployed in a 3D space. We want to devise a mechanism that keeps some nodes active and puts other nodes into sleep so that the number of ac...

Until recently, the solution to the Kelvin problem of nding a partition of R 3 into equal-volume cells with the least surface area was believed to be tessellation by the truncated octahe-dron. In 1994, D. Weaire and R. Phelan described a partition that outperformed the truncated octahedron partition in this respect. In this paper, we show that the eeective normalized moment of inertia (NMI) of ...

Gold-copper (Au-Cu) phases were employed already by pre-Columbian civilizations, essentially in decorative arts, whereas nowadays, they emerge in nanotechnology as an important catalyst. The knowledge of the phase diagram is critical to understanding the performance of a material. However, experimental determination of nanophase diagrams is rare because calorimetry remains quite challenging at ...

We show that a family of multivariate polynomials recently introduced by Bessenrodt and Stanley can be expressed as solution of the octahedron recurrence with suitable initial data. This leads to generalizations and explicit expressions as path or dimer partition functions.

We prove that the Dehn invariants of any Bricard octahedron remain constant during the flex and that the Strong Bellows Conjecture holds true for the Steffen flexible polyhedron. Mathematics Subject Classification (2000): 52C25.

We consider complex curves of genus zero and answer the above riddle. Namely, the lemniscate of Bernoulli, which has obvious four-fold symmetry, actually has the octahedral group as its symmetry group, and may in fact be characterized by this symmetry.