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Tetrad (geometry puzzle)

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The solutions with four congruent tiles include some with five sides. However, their placement surrounds an uncovered hole in the plane. Among solutions without holes, the ones with the fewest possible sides are given by a hexagon identified by Scott Kim as a student at Stanford University. It is not
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Kim's solution has 16 vertices, while some of the pentagon solutions have as few as 11 vertices. It is not known whether fewer vertices are possible.
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disjoint planar regions in the plane, each pair sharing a finite portion of common boundary. It was named by Michael R. W. Buckley in 1975 in the
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Application of IT in Mathematical Proofs and in Checking of Results of Pupils’ Research
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known whether five-sided solutions without holes are possible.
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Tetrad with one central region and 3 surrounding ones
703: 463: 686: 400: 442: 693: 679: 407: 393: 15: 575: 573: 571: 595: 593: 591: 704: 568: 645: 588: 433:Journal of Recreational Mathematics 13: 14: 733: 609: 581:Penrose Tiles to Trapdoor ciphers 649: 638:Juris ČERŅENOKS, Andrejs CIBULIS 549: 537: 525: 513: 501: 489: 452: 58: 28: 19: 600:Further Questions about Tetrads 1: 620:Polyomino and Polynar Tetrads 561: 665:. You can help Knowledge by 484:) solutions, with no holes. 468:Gardner offered a number of 464:Congruent polyform solutions 7: 10: 738: 644: 636:Tetrads and their Counting 439:, other enclosed regions. 443:Fewest sides and vertices 369:Nikoli puzzle types 46:Part of a series on 583:, 1989, p.121-123 374:Puzzle video games 359:Impossible puzzles 250:Puzzle video games 674: 673: 427:is a set of four 417: 416: 273: 272: 41: 40: 729: 695: 688: 681: 659:geometry-related 653: 646: 616:Polyform Tetrads 603: 602:by Walter Trump 597: 586: 579:Martin Gardner, 577: 553: 541: 529: 517: 505: 493: 456: 429:simply connected 409: 402: 395: 364:Maze video games 353: 313:Packing problems 308:Optical illusion 286: 75: 74: 71: 62: 43: 42: 32: 23: 16: 737: 736: 732: 731: 730: 728: 727: 726: 702: 701: 700: 699: 642: 625:A Tetrad Puzzle 612: 607: 606: 598: 589: 578: 569: 564: 557: 554: 545: 542: 533: 530: 521: 518: 509: 506: 497: 494: 466: 445: 413: 384: 383: 354: 351: 344: 343: 342: 323:Problem solving 287: 282: 275: 274: 207: 154:Disentanglement 72: 69: 33: 24: 12: 11: 5: 735: 725: 724: 722:Geometry stubs 719: 714: 712:Tiling puzzles 698: 697: 690: 683: 675: 672: 671: 654: 640: 639: 633: 628: 622: 611: 610:External links 608: 605: 604: 587: 566: 565: 563: 560: 559: 558: 555: 548: 546: 543: 536: 534: 531: 524: 522: 519: 512: 510: 507: 500: 498: 495: 488: 465: 462: 458: 457: 444: 441: 415: 414: 412: 411: 404: 397: 389: 386: 385: 382: 381: 376: 371: 366: 361: 355: 350: 349: 346: 345: 341: 340: 335: 330: 325: 320: 315: 310: 305: 300: 295: 289: 288: 281: 280: 277: 276: 271: 270: 264: 263: 262: 261: 253: 252: 246: 245: 244: 243: 238: 230: 229: 219: 218: 217: 216: 205: 200: 195: 187: 186: 185: 184: 179: 174: 169: 161: 156: 151: 146: 138: 137: 131: 130: 129: 128: 126:Self-reference 123: 118: 113: 105: 104: 98: 97: 96: 95: 90: 82: 81: 73: 68: 67: 64: 63: 55: 54: 48: 47: 39: 38: 34:Tetrad with a 26: 9: 6: 4: 3: 2: 734: 723: 720: 718: 715: 713: 710: 709: 707: 696: 691: 689: 684: 682: 677: 676: 670: 668: 664: 661:article is a 660: 655: 652: 648: 647: 643: 637: 634: 632: 629: 626: 623: 621: 617: 614: 613: 601: 596: 594: 592: 585: 582: 576: 574: 572: 567: 552: 547: 540: 535: 528: 523: 516: 511: 504: 499: 492: 487: 486: 485: 483: 479: 475: 471: 461: 455: 451: 450: 449: 440: 438: 434: 430: 426: 422: 410: 405: 403: 398: 396: 391: 390: 388: 387: 380: 379:Puzzle topics 377: 375: 372: 370: 367: 365: 362: 360: 357: 356: 348: 347: 339: 336: 334: 331: 329: 326: 324: 321: 319: 316: 314: 311: 309: 306: 304: 301: 299: 296: 294: 291: 290: 285: 279: 278: 269: 266: 265: 260: 257: 256: 255: 254: 251: 248: 247: 242: 239: 237: 234: 233: 232: 231: 228: 224: 221: 220: 214: 210: 206: 204: 201: 199: 196: 194: 191: 190: 189: 188: 183: 180: 178: 175: 173: 170: 168: 166: 162: 160: 157: 155: 152: 150: 147: 145: 142: 141: 140: 139: 136: 133: 132: 127: 124: 122: 119: 117: 114: 112: 109: 108: 107: 106: 103: 100: 99: 94: 91: 89: 86: 85: 84: 83: 80: 77: 76: 66: 65: 61: 57: 56: 53: 50: 49: 45: 44: 37: 31: 27: 22: 18: 17: 717:Tessellation 667:expanding it 656: 641: 627:7 April 2020 580: 544:26 triangles 532:22 triangles 520:10 triangles 467: 459: 446: 436: 424: 418: 293:Brain teaser 164: 149:Construction 35: 268:Metapuzzles 144:Combination 706:Categories 562:References 556:4 hexagons 508:12 squares 496:11 squares 478:polyiamond 328:Puzzlehunt 213:Logic maze 135:Mechanical 121:Logic grid 111:Dissection 474:polyomino 333:Syllogism 236:Crossword 116:Induction 93:Situation 470:polyform 421:geometry 167:problems 79:Guessing 482:polyhex 318:Paradox 298:Dilemma 211: ( 198:Sliding 172:Folding 52:Puzzles 480:, and 425:tetrad 284:Topics 241:Sudoku 227:Number 182:Tiling 88:Riddle 657:This 437:holes 352:Lists 259:Mazes 203:Chess 177:Stick 102:Logic 70:Types 663:stub 618:and 423:, a 338:Tale 303:Joke 225:and 223:Word 209:Maze 193:Tour 159:Lock 36:hole 419:In 708:: 590:^ 570:^ 476:, 165:Go 694:e 687:t 680:v 669:. 472:( 408:e 401:t 394:v 215:)

Index



Puzzles
Jigsaw piece
Guessing
Riddle
Situation
Logic
Dissection
Induction
Logic grid
Self-reference
Mechanical
Combination
Construction
Disentanglement
Lock
Go problems
Folding
Stick
Tiling
Tour
Sliding
Chess
Maze
Logic maze
Word
Number
Crossword
Sudoku

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