This paper gives a proof of the classical honeycomb conjecture: any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal honeycomb tiling.

A form of cystic lung, characterized by numerous, widespread and usually small cavities, is a wellrecognized though apparently uncommon condition, which, according to earlier accounts, occurred especially in children (Sharkey, 1894; Tooth, 1897; Fletcher, 1901; Bernstein, 1905). Such lungs were described by Fowler and Godlee (1898) as having a worm-eaten or honeycomb appearance. Sharkey and Fle...

Recently Beaton, de Gier and Guttmann proved a conjecture of Batchelor and Yung that the critical fugacity of self-avoiding walks interacting with (alternate) sites on the surface of the honeycomb lattice is 1 + √ 2. A key identity used in that proof depends on the existence of a parafermionic observable for self-avoiding walks interacting with a surface on the honeycomb lattice. Despite the ab...

High-aspect ratio micro- and nano-structures have been used for the production of a variety of applications. In this paper, we describe a simple and cost-effective approach to fabricate an arrayed microarchitecture with an ultra-high aspect ratio using soft materials. The shapes and sizes of the honeycomb structure can be easily modulated by changing the dimensions and position of the base moul...

Honeycomb core sandwich panels have found extensive applications particularly in the aerospace and naval industries. In view of the recent interest in alternative, yet strong and lightweight materials, honeycomb cores are manufactured from sisal fiber-reinforced polypropylene (PP) composites and the out-ofplane compressive behaviour of these cores is investigated. The cell wall material is mode...

Abstract The thermal analysis is performed on a heated Inconel 617 honeycomb-core sandwich panel. Sandwich panel is supported at its four edges with spar-like sub-structures that acted as heat sinks, which are generally not considered in the classical analysis. One side of the panel is subjected to a heat flux on the surface. Two types of surface heating were considered: (1) hexagonal honeycomb...

We report the structures and physical properties of two new iridates, NaIrO3 and Sr3CaIr2O9, both of which contain continuous two-dimensional honeycomb connectivity. NaIrO3 is produced by room temperature oxidative deintercalation of sodium from Na2IrO3, and contains edge-sharing IrO6 octahedra that form a planar honeycomb lattice. Sr3CaIr2O9, produced via conventional solid-state synthesis, ho...

Herein, we report honeycomb nanostructured single crystalline hexagonal WO(3) (h-WO(3)) thin films in order to improve electrochromic performance. In the present investigation, honeycomb nanostructured WO(3) with different unit size and nanowire array with highly nanocrystalline frameworks have been synthesized via a hydrothermal technique. The influence of hydrothermal reaction time on the hon...

The creation of engineered 3D microtissues has attracted prodigious interest because of the fact that this microtissue structure is able to mimic in vivo environments. Such microtissues can be applied extensively in the fields of regenerative medicine and tissue engineering, as well as in drug and toxicity screening. Here, we develop a novel method of fabricating a large number of dense honeyco...

Honeycomb (2D) and diamond (3D) networks constitute alternatives to mesh and torus architectures for paraUel processing. When wraparound links are zncluded in honeycomb and diamond networks, the resulting structures can be viewed as having been derived via a systematic pruning scheme applied to 2D and 3D tori. respectively. Link removal. which is performed along a diagonal pruning direction, pr...