Look for examples of tessellations in students’ environment such as. Mosaic tiles can be created from fired clay, or cobblestones created from concrete. Tessellation might fit well with efforts to beautify the school environment. We expect the example demonstrated in this work will stimulate interest in computationally identifying novel 2D materials from a variety of bulk materials with the pyrite structure. For example, tessellations are prominent in Islamic art traditions, and in tapa cloth designs from Pacific nations. We observe no spin-helical Dirac cone states, therefore ruling out single-layer PtP 2 as a topological insulator. ![]() Learn more about tessellation & see examples in math and art. Finally, we study the surface states of single-layer PtP 2 and consider the spin-orbit coupling. Tessellation, or tiling, is a repeating pattern of shapes over a surface without overlaps or gaps. We further study the bonding characteristics of this novel single-layer material by computing the Bader charge transfer, the electron localization function, and the crystal orbit overlap population, which show mixed P-P covalent bonding and Pt-P ionic bonding, with the former being stronger. By contrast, using the standard Perdew-Burke-Ernzerhof functional leads to the conclusion of single-layer PtP 2 being metallic. We also observe a reduction in the band gaps of PtP 2 from bulk to single layer using the Heyd-Scuseria-Ernzerhof (HSE) hybrid density functional, and the band gap type switches from indirect to direct. Unlike previously reported single-layer materials such as PdSe 2 with a buckled, pentagonal structure-strictly speaking, not belonging to the Cairo tessellation, we find that single-layer PtP 2 is completely planar exhibiting dynamically stable phonon modes. ![]() We use this hidden tessellation along with density functional theory calculations to examine the possibility of obtaining a two-dimensional (2D) material with the Cairo tessellation from the bulk, using PtP 2 as an example. A checkerboard is the simplest example of this: It comprises square tiles in two contrasting colors (usually black and white) that could repeat forever. For each seed there is a corresponding region, called. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). It can be classified also as a tessellation. We reveal the hidden, layered Cairo tessellations in the pyrite structure with a general chemical formula A B 2 and space group p a 3 ¯. An example of a hexagonal tessellation pattern that you’ll find in day-to-day life is a honeycomb. In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. ![]() The Cairo tessellation refers to a pattern of type 2 pentagons that can tile an infinite plane without creating a gap or overlap.
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