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Hexagonal lattice | Wallpaper group p6m | Unit cell |
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The hexagonal lattice (sometimes called triangular lattice) is one of the five two-dimensional Bravais lattice types.[1] The symmetry category of the lattice is wallpaper group p6m. The primitive translation vectors of the hexagonal lattice form an angle of 120° and are of equal lengths,
The reciprocal lattice of the hexagonal lattice is a hexagonal lattice in reciprocal space with orientation changed by 90° and primitive lattice vectors of length
Honeycomb point set
[edit]![](https://upload.wikimedia.org/wikipedia/commons/thumb/4/46/Honeycomb_lattice_-_hexagonal_lattice_with_a_two-atom_basis.svg/220px-Honeycomb_lattice_-_hexagonal_lattice_with_a_two-atom_basis.svg.png)
The honeycomb point set is a special case of the hexagonal lattice with a two-atom basis.[1] The centers of the hexagons of a honeycomb form a hexagonal lattice, and the honeycomb point set can be seen as the union of two offset hexagonal lattices.
In nature, carbon atoms of the two-dimensional material graphene are arranged in a honeycomb point set.
Crystal classes
[edit]The hexagonal lattice class names, Schönflies notation, Hermann-Mauguin notation, orbifold notation, Coxeter notation, and wallpaper groups are listed in the table below.
Geometric class, point group | Wallpaper groups | ||||
---|---|---|---|---|---|
Schön. | Intl | Orb. | Cox. | ||
C3 | 3 | (33) | [3]+ | p3 (333) |
|
D3 | 3m | (*33) | [3] | p3m1 (*333) |
p31m (3*3) |
C6 | 6 | (66) | [6]+ | p6 (632) |
|
D6 | 6mm | (*66) | [6] | p6m (*632) |
See also
[edit]- Square lattice
- Hexagonal tiling
- Close-packing
- Centered hexagonal number
- Eisenstein integer
- Voronoi diagram
- Hermite constant
References
[edit]- ^ a b Rana, Farhan. "Lattices in 1D, 2D, and 3D" (PDF). Cornell University. Archived (PDF) from the original on 2020-12-18.
Well, that’s interesting to know that Psilotum nudum are known as whisk ferns. Psilotum nudum is the commoner species of the two. While the P. flaccidum is a rare species and is found in the tropical islands. Both the species are usually epiphytic in habit and grow upon tree ferns. These species may also be terrestrial and grow in humus or in the crevices of the rocks.
View the detailed Guide of Psilotum nudum: Detailed Study Of Psilotum Nudum (Whisk Fern), Classification, Anatomy, Reproduction