special case of the hexagonal lattice with a two-atom basis. The centers of the hexagons of a honeycomb form a hexagonal lattice, and the honeycomb point...

crystallography, the hexagonal crystal family is one of the six crystal families, which includes two crystal systems (hexagonal and trigonal) and two lattice systems...

hexagonal), four crystal families (oblique, rectanguar, square, hexagonal), and four lattice systems (oblique, rectangular, square, and hexagonal)....

called hexagonal diamond in reference to the crystal structure, is an allotrope of carbon with a hexagonal lattice, as opposed to the cubical lattice of conventional...

full list of subgroups is available. For example, below the hexagonal/triangular lattice is given twice, with full 6-fold and a half 3-fold reflectional...

dot in a hexagonal lattice. The following figures illustrate this arrangement for the first four centered hexagonal numbers: Centered hexagonal numbers...

In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex...

simple hexagonal Bravais lattice with lattice constants a {\textstyle a} and c {\textstyle c} is another simple hexagonal lattice with lattice constants...

In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice is broken up into Brillouin zones...

face-centered cubic lattice – with different orientation to the ground. Hexagonal close-packing would result in a six-sided pyramid with a hexagonal base. The cannonball...

present at all, form a regular hexagonal lattice which is the translate of the translational lattice. Scaling of a lattice divides the number of points...

Asgardia the space nation. 1, 7, and 19-circle hexagonal variant In the examples below the pattern has a hexagonal outline, and is further circumscribed. Leonardo...

(1646–1715). It is a mathematical problem that involves a hexagonal lattice, like the hexagonal pattern on some tortoises' shells, to the (N) vertices of...

examples are a triangular lattice with or without connecting lines, and a hexagonal tiling with one color for outlining the hexagons and one for the background...

lattice. It occurs also in the crystal structures of certain minerals. Conway calls it a hexadeltille, combining alternate elements from a hexagonal tiling...

the sinc function for the hexagonal lattice is a function whose Fourier transform is the indicator function of the unit hexagon in the frequency space....

the hexagonal lattice with a density of π 3 3 ≈ 0.6046 {\displaystyle {\frac {\pi }{3{\sqrt {3}}}}\approx 0.6046} and the tetrahedral lattice with a...

appropriate. Hexagonal lattices were introduced to alleviate sharp turns of adjacent residues in triangular lattices. Hexagonal lattices with diagonals...

the 4 remaining lattice categories: square, hexagonal, rectangular, and centered rectangular. Thus altogether there are 5 Bravais lattices in 2 dimensions...

by Duminil-Copin and Smirnov that the connective constant of the hexagonal lattice has the precise value 2 + 2 {\displaystyle {\sqrt {2+{\sqrt {2}}}}}...

together to form a cubic lattice of tetrahedra), graphite (the carbon atoms are bonded together in sheets of a hexagonal lattice), graphene (single sheets...

crystallography for lattice planes in crystal (Bravais) lattices. In particular, a family of lattice planes of a given (direct) Bravais lattice is determined...

cell for any given lattice. It is the locus of points in space that are closer to that lattice point than to any of the other lattice points. A Wigner–Seitz...

more enlightening picture emerges if we represent it in terms of a hexagonal lattice instead; this is the Tonnetz of Hugo Riemann, discovered independently...

the mathematical discipline of order theory, a complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every...

The Hexagonal Efficient Coordinate System (HECS), formerly known as Array Set Addressing (ASA), is a coordinate system for hexagonal grids that allows...

example of a sampling lattice in two dimensional space is a hexagonal lattice depicted in Figure 1. The corresponding reciprocal lattice is shown in Figure...

whole trigonal system.) The hexagonal lattice system is larger than the hexagonal crystal system, and consists of the hexagonal crystal system together with...

of many hexagonal crystal system minerals Hexagonal barn The Hexagon, a hexagonal theatre in Reading, Berkshire Władysław Gliński's hexagonal chess Pavilion...

fraction is 85.3542%, if only hexagonal lattice clusters are disallowed, and 85.2514% if one disallows also deformed square lattice clusters. An analytical...