Hexagonal lattice

<h2 id="honeycomb-point-set">Honeycomb point set</h2>

<p>The honeycomb point set is a special case of the hexagonal lattice with a two-atom basis.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a>  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.
</p><p>In nature, <a href="/facts/Carbon/ukrgQexo">carbon</a> atoms of the two-dimensional material <a href="/facts/Graphene/QDGUBaPt">graphene</a> are arranged in a honeycomb point set.
</p>

<h2 id="crystal-classes">Crystal classes</h2>
<p>The <i>hexagonal lattice</i> class names, <a href="/facts/Sch%25C3%25B6nflies_notation/c4y0GtEt">Schönflies notation</a>, <a href="/facts/Hermann-Mauguin_notation/NGHDFXKC">Hermann-Mauguin notation</a>, <a href="/facts/Orbifold_notation/HCbBoa2J">orbifold notation</a>, <a href="/facts/Coxeter_notation/ArUw6goe">Coxeter notation</a>, and <a href="/facts/Wallpaper_groups/egxEaC8q">wallpaper groups</a> are listed in the table below.
</p>
<table><tbody><tr><th colspan="4">Geometric class, <a href="/facts/Point_group/41NSqUN6">point group</a></th><th rowspan="2" colspan="2">Wallpaper groups</th></tr><tr><th><a href="/facts/Sch%25C3%25B6nflies_notation/c4y0GtEt">Schön.</a></th><th><a href="/facts/Hermann-Mauguin_notation/NGHDFXKC">Intl</a></th><th><a href="/facts/Orbifold_notation/HCbBoa2J">Orb.</a></th><th><a href="/facts/Coxeter_notation/ArUw6goe">Cox.</a></th></tr><tr><td>C3</td><td>3</td><td>(33)</td><td>[3]+</td><td>p3(333)</td><td> </td></tr><tr><td>D3</td><td>3m</td><td>(*33)</td><td>[3]</td><td>p3m1(*333)</td><td>p31m(3*3)</td></tr><tr><td>C6</td><td>6</td><td>(66)</td><td>[6]+</td><td>p6(632)</td><td> </td></tr><tr><td>D6</td><td>6mm</td><td>(*66)</td><td>[6]</td><td>p6m(*632)</td><td> </td></tr></tbody></table>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Square_lattice/mcVtpcQK">Square lattice</a></li>
<li><a href="/facts/Hexagonal_tiling/HwG5F0YH">Hexagonal tiling</a></li>
<li><a href="/facts/Close-packing/AqL1HUxe">Close-packing</a></li>
<li><a href="/facts/Centered_hexagonal_number/M5eUvBGG">Centered hexagonal number</a></li>
<li><a href="/facts/Eisenstein_integer/UGQmFI8c">Eisenstein integer</a></li>
<li><a href="/facts/Voronoi_diagram/AhQY5LD8">Voronoi diagram</a></li>
<li><a href="/facts/Hermite_constant/nq713k79">Hermite constant</a></li></ul>

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<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Rana, Farhan. "Lattices in 1D, 2D, and 3D" (PDF). Cornell University. Archived (PDF) from the original on 2020-12-18. <a href="https://courses.cit.cornell.edu/ece407/Lectures/handout4.pdf" target="_blank">https://courses.cit.cornell.edu/ece407/Lectures/handout4.pdf</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Rana, Farhan. "Lattices in 1D, 2D, and 3D" (PDF). Cornell University. Archived (PDF) from the original on 2020-12-18. <a href="https://courses.cit.cornell.edu/ece407/Lectures/handout4.pdf" target="_blank">https://courses.cit.cornell.edu/ece407/Lectures/handout4.pdf</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
</ol>

Hexagonal lattice open-in-new

Hexagonal lattice