Knowledge (XXG)

Order-6 triangular hosohedral honeycomb

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of central spherical projection, with all edges being projected into circles. Seen below triangular tiling edges are colored into 3 parallel sets for each hemisphere.
193:{2,3} around each edge. It is a degenerate honeycomb in Euclidean space, but can be seen as a projection onto the sphere. Its vertex figure, a 387: 312: 292: 256: 246: 52: 297: 332: 322: 302: 276: 266: 82: 72: 62: 285: 327: 317: 307: 271: 261: 251: 77: 67: 57: 407: 354: 144: 359: 27: 226: 205: 215: 391: 151: 182: 341: 186: 97: 34: 383: 375: 194: 128: 281: 44: 401: 133: 178: 190: 93: 242:
This honeycomb can be truncated as t{2,3,6} or {}Ă—{3,6}, Coxeter diagram
170: 118: 379: 108: 15: 8: 18: 210: 19:Order-6 triangular hosohedral honeycomb 175:order-6 triangular hosohedral honeycomb 392:Regular Honeycombs in Hyperbolic Space 372:The Beauty of Geometry: Twelve Essays 7: 145:Order-2 hexagonal tiling honeycomb 14: 340: 330: 325: 320: 315: 310: 305: 300: 295: 290: 274: 269: 264: 259: 254: 249: 244: 225: 214: 132: 96: 80: 75: 70: 65: 60: 55: 50: 159: 150: 140: 124: 114: 104: 89: 43: 33: 23: 286:triangular prismatic honeycomb 1: 355:Order-7 tetrahedral honeycomb 189:{2,3,6}. It has 6 triangular 374:(1999), Dover Publications, 223: 212: 197:is seen on each hemisphere. 28:Degenerate regular honeycomb 424: 360:List of regular polytopes 206:Stereographic projections 177:a regular space-filling 280:, seen as one layer of 408:Regular 3-honeycombs 231:Centered on equator 238:Related honeycombs 282:triangular prisms 235: 234: 220:Centered on pole 195:triangular tiling 167: 166: 415: 344: 335: 334: 333: 329: 328: 324: 323: 319: 318: 314: 313: 309: 308: 304: 303: 299: 298: 294: 293: 279: 278: 277: 273: 272: 268: 267: 263: 262: 258: 257: 253: 252: 248: 247: 229: 218: 211: 136: 100: 85: 84: 83: 79: 78: 74: 73: 69: 68: 64: 63: 59: 58: 54: 53: 45:Coxeter diagrams 16: 423: 422: 418: 417: 416: 414: 413: 412: 398: 397: 368: 351: 331: 326: 321: 316: 311: 306: 301: 296: 291: 289: 275: 270: 265: 260: 255: 250: 245: 243: 240: 230: 219: 203: 187:Schläfli symbol 131: 81: 76: 71: 66: 61: 56: 51: 49: 35:Schläfli symbol 12: 11: 5: 421: 419: 411: 410: 400: 399: 396: 395: 367: 364: 363: 362: 357: 350: 347: 346: 345: 239: 236: 233: 232: 222: 221: 202: 199: 165: 164: 161: 157: 156: 154: 148: 147: 142: 138: 137: 126: 122: 121: 116: 112: 111: 106: 102: 101: 91: 87: 86: 47: 41: 40: 37: 31: 30: 25: 21: 20: 13: 10: 9: 6: 4: 3: 2: 420: 409: 406: 405: 403: 393: 390:(Chapter 10, 389: 388:0-486-40919-8 385: 381: 377: 373: 370: 369: 365: 361: 358: 356: 353: 352: 348: 343: 339: 338: 337: 287: 283: 237: 228: 224: 217: 213: 209: 207: 200: 198: 196: 192: 188: 184: 180: 176: 172: 162: 158: 155: 153: 152:Coxeter group 149: 146: 143: 139: 135: 130: 127: 125:Vertex figure 123: 120: 117: 113: 110: 107: 103: 99: 95: 92: 88: 48: 46: 42: 38: 36: 32: 29: 26: 22: 17: 371: 241: 204: 179:tessellation 174: 168: 284:, within a 115:Edge figure 366:References 160:Properties 191:hosohedra 183:honeycomb 402:Category 380:99-35678 349:See also 171:geometry 163:Regular 39:{2,3,6} 185:) with 386:  378:  201:Images 173:, the 129:{3,6} 105:Faces 94:{2,3} 90:Cells 384:ISBN 376:LCCN 181:(or 141:Dual 24:Type 169:In 119:{6} 109:{2} 404:: 382:, 336:. 288:, 394:)

Index

Degenerate regular honeycomb
Schläfli symbol
Coxeter diagrams
{2,3}

{2}
{6}
{3,6}

Order-2 hexagonal tiling honeycomb
Coxeter group
geometry
tessellation
honeycomb
Schläfli symbol
hosohedra
triangular tiling
Stereographic projections


triangular prisms
triangular prismatic honeycomb

Order-7 tetrahedral honeycomb
List of regular polytopes
LCCN
99-35678
ISBN
0-486-40919-8
Regular Honeycombs in Hyperbolic Space

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