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Tesseractic honeycomb honeycomb

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324: 309: 354: 279: 371: 264: 339: 294: 465: 384: 145: 552: 534: 221: 150: 236: 213: 203: 163: 120: 62: 231: 251: 241: 226: 193: 183: 173: 155: 140: 130: 112: 102: 92: 82: 72: 208: 568: 246: 198: 188: 178: 168: 135: 125: 107: 97: 87: 77: 67: 492: 508: 484: 35: 525: 488: 477: 457: 267: 437: 496: 453: 42: 548: 530: 374: 323: 308: 555:(Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II, III, IV, V, p212-213) 429: 421: 353: 278: 370: 54: 540: 520: 445: 263: 562: 461: 391: 364: 433: 449: 282: 417: 327: 537:. (Tables I and II: Regular polytopes and honeycombs, pp. 294–296) 357: 338: 293: 312: 18: 342: 297: 26: 491:, {4,4,3}, in 3-dimensional hyperbolic space, and the 495:, {∞,3} of 2-dimensional hyperbolic space, each with 487:, {4,3,4,3}, in 4-dimensional hyperbolic space, 476:It is related to the regular Euclidean 4-space 8: 21: 529:, 3rd. ed., Dover Publications, 1973. 545:The Beauty of Geometry: Twelve Essays 7: 483:It is analogous to the paracompact 466:order-4 24-cell honeycomb honeycomb 385:Order-4 24-cell honeycomb honeycomb 14: 369: 352: 337: 322: 307: 292: 277: 262: 249: 244: 239: 234: 229: 224: 219: 211: 206: 201: 196: 191: 186: 181: 176: 171: 166: 161: 153: 148: 143: 138: 133: 128: 123: 118: 110: 105: 100: 95: 90: 85: 80: 75: 70: 65: 60: 22:Tesseractic honeycomb honeycomb 426:tesseractic honeycomb honeycomb 406: 390: 380: 363: 348: 333: 318: 303: 288: 273: 258: 53: 41: 31: 1: 36:Hyperbolic regular honeycomb 547:, Dover Publications, 1999 428:is one of five paracompact 585: 493:order-3 apeirogonal tiling 456:{4,3,3,4,3}, it has three 509:List of regular polytopes 485:cubic honeycomb honeycomb 460:around each cell. It is 444:because it has infinite 489:square tiling honeycomb 448:, with all vertices as 458:tesseractic honeycombs 569:Honeycombs (geometry) 478:tesseractic honeycomb 497:hypercube honeycomb 452:at infinity. With 16:Geometrical concept 472:Related honeycombs 422:hyperbolic 5-space 526:Regular Polytopes 414: 413: 576: 440:). It is called 398: 373: 356: 341: 326: 311: 296: 281: 266: 254: 253: 252: 248: 247: 243: 242: 238: 237: 233: 232: 228: 227: 223: 222: 216: 215: 214: 210: 209: 205: 204: 200: 199: 195: 194: 190: 189: 185: 184: 180: 179: 175: 174: 170: 169: 165: 164: 158: 157: 156: 152: 151: 147: 146: 142: 141: 137: 136: 132: 131: 127: 126: 122: 121: 115: 114: 113: 109: 108: 104: 103: 99: 98: 94: 93: 89: 88: 84: 83: 79: 78: 74: 73: 69: 68: 64: 63: 19: 584: 583: 579: 578: 577: 575: 574: 573: 559: 558: 517: 505: 474: 454:Schläfli symbol 401: 396: 250: 245: 240: 235: 230: 225: 220: 218: 217: 212: 207: 202: 197: 192: 187: 182: 177: 172: 167: 162: 160: 154: 149: 144: 139: 134: 129: 124: 119: 117: 116: 111: 106: 101: 96: 91: 86: 81: 76: 71: 66: 61: 59: 55:Coxeter diagram 48: 43:Schläfli symbol 17: 12: 11: 5: 582: 580: 572: 571: 561: 560: 557: 556: 538: 516: 513: 512: 511: 504: 501: 473: 470: 446:vertex figures 432:space-filling 412: 411: 408: 404: 403: 399: 394: 388: 387: 382: 378: 377: 367: 361: 360: 350: 346: 345: 335: 331: 330: 320: 316: 315: 305: 301: 300: 290: 286: 285: 275: 271: 270: 260: 256: 255: 57: 51: 50: 45: 39: 38: 33: 29: 28: 24: 23: 15: 13: 10: 9: 6: 4: 3: 2: 581: 570: 567: 566: 564: 554: 553:0-486-40919-8 550: 546: 542: 539: 536: 535:0-486-61480-8 532: 528: 527: 522: 519: 518: 514: 510: 507: 506: 502: 500: 498: 494: 490: 486: 481: 480:, {4,3,3,4}. 479: 471: 469: 467: 463: 459: 455: 451: 447: 443: 439: 435: 434:tessellations 431: 427: 423: 419: 409: 405: 395: 393: 392:Coxeter group 389: 386: 383: 379: 376: 372: 368: 366: 365:Vertex figure 362: 359: 355: 351: 347: 344: 340: 336: 332: 329: 325: 321: 317: 314: 310: 306: 302: 299: 295: 291: 287: 284: 280: 276: 272: 269: 265: 261: 257: 58: 56: 52: 46: 44: 40: 37: 34: 30: 25: 20: 544: 524: 482: 475: 450:ideal points 441: 425: 415: 442:paracompact 349:Edge figure 334:Face figure 319:Cell figure 47:{4,3,3,4,3} 27:(No image) 515:References 438:honeycombs 407:Properties 375:{3,3,4,3} 268:{4,3,3,4} 563:Category 503:See also 499:facets. 418:geometry 410:Regular 49:{4,3,3} 541:Coxeter 521:Coxeter 464:to the 430:regular 416:In the 358:{3,4,3} 283:{4,3,3} 274:4-faces 259:5-faces 551:  533:  424:, the 343:{4,3} 304:Faces 298:{4,3} 289:Cells 549:ISBN 531:ISBN 462:dual 436:(or 381:Dual 32:Type 420:of 402:, 328:{3} 313:{4} 565:: 543:, 523:, 468:. 159:↔ 400:5 397:R

Index

Hyperbolic regular honeycomb
Schläfli symbol
Coxeter diagram

{4,3,3,4}

{4,3,3}

{4,3}

{4}

{3}

{4,3}

{3,4,3}
Vertex figure

{3,3,4,3}
Order-4 24-cell honeycomb honeycomb
Coxeter group
geometry
hyperbolic 5-space
regular
tessellations
honeycombs
vertex figures
ideal points
Schläfli symbol

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