• Thumbnail for Hexagonal lattice
    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...
    5 KB (224 words) - 07:00, 4 February 2024
  • Thumbnail for Hexagonal crystal family
    crystallography, the hexagonal crystal family is one of the six crystal families, which includes two crystal systems (hexagonal and trigonal) and two lattice systems...
    18 KB (1,485 words) - 16:46, 28 October 2024
  • Thumbnail for Lattice (group)
    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...
    17 KB (2,289 words) - 23:00, 6 May 2025
  • Thumbnail for Lonsdaleite
    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...
    22 KB (2,049 words) - 11:37, 9 June 2025
  • Thumbnail for Crystal system
    hexagonal), four crystal families (oblique, rectanguar, square, hexagonal), and four lattice systems (oblique, rectangular, square, and hexagonal)....
    30 KB (1,458 words) - 22:16, 30 May 2025
  • Thumbnail for Centered hexagonal number
    dot in a hexagonal lattice. The following figures illustrate this arrangement for the first four centered hexagonal numbers: Centered hexagonal numbers...
    9 KB (728 words) - 14:40, 18 January 2025
  • Thumbnail for Reciprocal lattice
    simple hexagonal Bravais lattice with lattice constants a {\textstyle a} and c {\textstyle c} is another simple hexagonal lattice with lattice constants...
    33 KB (5,496 words) - 08:15, 17 April 2025
  • Thumbnail for Hexagonal tiling
    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...
    20 KB (1,603 words) - 22:05, 3 May 2025
  • Thumbnail for Brillouin zone
    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...
    11 KB (640 words) - 06:31, 24 September 2024
  • Thumbnail for Close-packing of equal spheres
    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...
    19 KB (2,428 words) - 23:15, 4 March 2025
  • Thumbnail for Rotational symmetry
    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...
    15 KB (1,606 words) - 06:43, 27 March 2025
  • 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...
    28 KB (2,216 words) - 16:01, 7 February 2025
  • Thumbnail for Hexagonal tortoise problem
    (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...
    2 KB (168 words) - 22:36, 18 January 2024
  • Thumbnail for Trihexagonal tiling
    lattice. It occurs also in the crystal structures of certain minerals. Conway calls it a hexadeltille, combining alternate elements from a hexagonal tiling...
    16 KB (1,625 words) - 23:23, 26 February 2025
  • Thumbnail for Wallpaper group
    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...
    65 KB (6,485 words) - 13:43, 16 April 2025
  • by Duminil-Copin and Smirnov that the connective constant of the hexagonal lattice has the precise value 2 + 2 {\displaystyle {\sqrt {2+{\sqrt {2}}}}}...
    13 KB (2,354 words) - 05:04, 28 May 2025
  • appropriate. Hexagonal lattices were introduced to alleviate sharp turns of adjacent residues in triangular lattices. Hexagonal lattices with diagonals...
    16 KB (1,998 words) - 21:26, 25 September 2024
  • Thumbnail for Sinc function
    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....
    23 KB (3,233 words) - 21:43, 23 May 2025
  • Thumbnail for Wigner–Seitz cell
    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...
    16 KB (1,495 words) - 15:19, 17 December 2024
  • Thumbnail for Allotropy
    together to form a cubic lattice of tetrahedra), graphite (the carbon atoms are bonded together in sheets of a hexagonal lattice), graphene (single sheets...
    31 KB (2,062 words) - 09:26, 27 May 2025
  • Thumbnail for Sphere packing
    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...
    28 KB (3,419 words) - 09:38, 3 May 2025
  • more enlightening picture emerges if we represent it in terms of a hexagonal lattice instead; this is the Tonnetz of Hugo Riemann, discovered independently...
    9 KB (1,375 words) - 15:25, 6 April 2020
  • Thumbnail for Miller index
    crystallography for lattice planes in crystal (Bravais) lattices. In particular, a family of lattice planes of a given (direct) Bravais lattice is determined...
    16 KB (2,457 words) - 09:34, 25 April 2025
  • Thumbnail for Bravais lattice
    the 4 remaining lattice categories: square, hexagonal, rectangular, and centered rectangular. Thus altogether there are 5 Bravais lattices in 2 dimensions...
    22 KB (2,438 words) - 14:16, 31 May 2025
  • Thumbnail for Complemented lattice
    the mathematical discipline of order theory, a complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every...
    9 KB (876 words) - 15:48, 30 May 2025
  • The Hexagonal Efficient Coordinate System (HECS), formerly known as Array Set Addressing (ASA), is a coordinate system for hexagonal grids that allows...
    14 KB (1,774 words) - 14:41, 15 April 2025
  • 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...
    16 KB (2,010 words) - 05:44, 12 July 2024
  • Thumbnail for Square lattice
    orchard Gaussian integer Hexagonal lattice Quincunx Square tiling Conway, John; Sloane, Neil J. A. (1999), Sphere Packings, Lattices and Groups, Springer...
    7 KB (552 words) - 07:20, 4 February 2024
  • Thumbnail for Space group
    whole trigonal system.) The hexagonal lattice system is larger than the hexagonal crystal system, and consists of the hexagonal crystal system together with...
    55 KB (4,240 words) - 12:59, 23 May 2025
  • fraction is 85.3542%, if only hexagonal lattice clusters are disallowed, and 85.2514% if one disallows also deformed square lattice clusters. An analytical...
    10 KB (1,221 words) - 15:53, 3 May 2025