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Order-4 24-cell honeycomb

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

Index

Hyperbolic regular honeycomb
Schläfli symbol
Coxeter diagram

{3,4,3}

{3,4}

{3}

{4}

{3,4}
Vertex figure

{4,3,4}
Cubic honeycomb honeycomb
Coxeter group
geometry
hyperbolic 4-space
regular
tessellations
honeycombs
vertex figures
ideal points
Schläfli symbol
24-cells
dual
cubic honeycomb honeycomb
24-cell honeycomb

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