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Hexagonal lattice

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The honeycomb point set is a 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 set can be seen as the union of two offset hexagonal lattices.
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of the hexagonal lattice is a hexagonal lattice in reciprocal space with orientation changed by 90° and primitive lattice vectors of length
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Honeycomb point set as a hexagonal lattice with a two-atom basis. The gray rhombus is a primitive cell. Vectors
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p6m. The primitive translation vectors of the hexagonal lattice form an angle of 120° and are of equal lengths,
228: 610: 647: 264: 235: 657: 637: 500: 765: 667: 626: 571: 363: 326: 20: 760: 539: 358: 322: 682: 8: 714: 505: 164: 368: 330: 515: 490: 373: 338: 334: 704: 605: 510: 81: 73: 724: 594: 485: 30: 37: 754: 495: 348: 718: 676: 303: 77: 563: 671: 651: 299: 661: 641: 631: 738: 728: 708: 687: 153:{\displaystyle |\mathbf {a} _{1}|=|\mathbf {a} _{2}|=a.} 44: 267: 238: 176: 93: 282: 253: 212: 152: 752: 213:{\displaystyle g={\frac {4\pi }{a{\sqrt {3}}}}.} 579: 586: 572: 227: 306:are arranged in a honeycomb point set. 753: 302:atoms of the two-dimensional material 223: 567: 352: 72:) is one of the five two-dimensional 533: 531: 593: 290:are primitive translation vectors. 16:One of the five 2D Bravais lattices 13: 312: 14: 777: 528: 737: 727: 717: 707: 686: 675: 670: 660: 650: 640: 630: 556:from the original on 2020-12-18. 537: 283:{\displaystyle \mathbf {a} _{2}} 270: 254:{\displaystyle \mathbf {a} _{1}} 241: 126: 101: 43: 36: 29: 341:are listed in the table below. 137: 120: 112: 95: 25: 1: 521: 611:Crystallographic point group 540:"Lattices in 1D, 2D, and 3D" 452: 428: 402: 378: 356: 7: 479: 80:category of the lattice is 10: 782: 18: 697: 619: 601: 501:Centered hexagonal number 346: 668:trigonal & hexagonal 327:Hermann-Mauguin notation 21:Hexagonal crystal family 19:Not to be confused with 291: 284: 255: 214: 154: 285: 256: 231: 215: 155: 265: 236: 174: 91: 55:Wallpaper group p6m 323:Schönflies notation 224:Honeycomb point set 547:Cornell University 506:Eisenstein integer 292: 280: 251: 210: 165:reciprocal lattice 150: 70:triangular lattice 68:(sometimes called 52:Hexagonal lattice 748: 747: 477: 476: 353:Wallpaper groups 347:Geometric class, 331:orbifold notation 319:hexagonal lattice 205: 202: 66:hexagonal lattice 62: 61: 773: 741: 731: 721: 711: 690: 679: 674: 664: 654: 644: 634: 620:Seven 3D systems 588: 581: 574: 565: 564: 558: 557: 555: 544: 535: 516:Hermite constant 491:Hexagonal tiling 344: 343: 339:wallpaper groups 335:Coxeter notation 289: 287: 286: 281: 279: 278: 273: 260: 258: 257: 252: 250: 249: 244: 219: 217: 216: 211: 206: 204: 203: 198: 192: 184: 159: 157: 156: 151: 140: 135: 134: 129: 123: 115: 110: 109: 104: 98: 47: 40: 33: 26: 781: 780: 776: 775: 774: 772: 771: 770: 766:Crystal systems 751: 750: 749: 744: 698:Four 2D systems 693: 615: 606:Bravais lattice 597: 595:Crystal systems 592: 562: 561: 553: 542: 536: 529: 524: 511:Voronoi diagram 482: 469: 457: 445: 433: 424: 419: 407: 395: 383: 315: 313:Crystal classes 309: 274: 269: 268: 266: 263: 262: 245: 240: 239: 237: 234: 233: 226: 197: 193: 185: 183: 175: 172: 171: 136: 130: 125: 124: 119: 111: 105: 100: 99: 94: 92: 89: 88: 82:wallpaper group 74:Bravais lattice 24: 17: 12: 11: 5: 779: 769: 768: 763: 761:Lattice points 746: 745: 743: 742: 732: 722: 712: 701: 699: 695: 694: 692: 691: 680: 665: 655: 645: 635: 623: 621: 617: 616: 614: 613: 608: 602: 599: 598: 591: 590: 583: 576: 568: 560: 559: 538:Rana, Farhan. 526: 525: 523: 520: 519: 518: 513: 508: 503: 498: 493: 488: 486:Square lattice 481: 478: 475: 474: 471: 466: 464: 461: 458: 455: 451: 450: 447: 442: 440: 437: 434: 431: 427: 426: 421: 416: 414: 411: 408: 405: 401: 400: 397: 392: 390: 387: 384: 381: 377: 376: 371: 366: 361: 355: 354: 351: 314: 311: 277: 272: 248: 243: 225: 222: 221: 220: 209: 201: 196: 191: 188: 182: 179: 161: 160: 149: 146: 143: 139: 133: 128: 122: 118: 114: 108: 103: 97: 60: 59: 56: 53: 49: 48: 41: 34: 15: 9: 6: 4: 3: 2: 778: 767: 764: 762: 759: 758: 756: 740: 736: 733: 730: 726: 723: 720: 716: 713: 710: 706: 703: 702: 700: 696: 689: 684: 681: 678: 673: 669: 666: 663: 659: 656: 653: 649: 646: 643: 639: 636: 633: 628: 625: 624: 622: 618: 612: 609: 607: 604: 603: 600: 596: 589: 584: 582: 577: 575: 570: 569: 566: 552: 548: 541: 534: 532: 527: 517: 514: 512: 509: 507: 504: 502: 499: 497: 496:Close-packing 494: 492: 489: 487: 484: 483: 472: 467: 465: 462: 459: 453: 448: 443: 441: 438: 435: 429: 422: 417: 415: 412: 409: 403: 398: 393: 391: 388: 385: 379: 375: 372: 370: 367: 365: 362: 360: 357: 350: 345: 342: 340: 336: 332: 328: 324: 321:class names, 320: 310: 307: 305: 301: 296: 275: 246: 230: 207: 199: 194: 189: 186: 180: 177: 170: 169: 168: 166: 147: 144: 141: 131: 116: 106: 87: 86: 85: 83: 79: 75: 71: 67: 57: 54: 51: 50: 46: 42: 39: 35: 32: 28: 27: 22: 734: 685:(isometric) 648:orthorhombic 546: 318: 316: 308: 297: 293: 162: 69: 65: 63: 715:rectangular 629:(anorthic) 349:point group 298:In nature, 76:types. The 755:Categories 658:tetragonal 638:monoclinic 522:References 58:Unit cell 735:hexagonal 627:triclinic 190:π 551:Archived 480:See also 304:graphene 78:symmetry 705:oblique 473:  470:(*632) 449:  420:(*333) 399:  725:square 446:(632) 425:(3*3) 396:(333) 359:Schön. 337:, and 300:carbon 683:cubic 554:(PDF) 543:(PDF) 463:(*66) 413:(*33) 439:(66) 423:p31m 418:p3m1 389:(33) 374:Cox. 369:Orb. 364:Intl 317:The 261:and 163:The 64:The 468:p6m 460:6mm 757:: 549:. 545:. 530:^ 444:p6 410:3m 394:p3 333:, 329:, 325:, 587:e 580:t 573:v 456:6 454:D 436:6 432:6 430:C 406:3 404:D 386:3 382:3 380:C 276:2 271:a 247:1 242:a 208:. 200:3 195:a 187:4 181:= 178:g 148:. 145:a 142:= 138:| 132:2 127:a 121:| 117:= 113:| 107:1 102:a 96:| 23:.

Index

Hexagonal crystal family



Bravais lattice
symmetry
wallpaper group
reciprocal lattice

carbon
graphene
Schönflies notation
Hermann-Mauguin notation
orbifold notation
Coxeter notation
wallpaper groups
point group
Schön.
Intl
Orb.
Cox.
Square lattice
Hexagonal tiling
Close-packing
Centered hexagonal number
Eisenstein integer
Voronoi diagram
Hermite constant

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