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Compound of twelve tetrahedra with rotational freedom

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369: 349: 329: 309: 289: 269: 249: 229: 209: 389: 29: 467: 375: 355: 335: 315: 295: 275: 255: 235: 167: 508: 368: 348: 328: 308: 288: 268: 248: 228: 482: 215: 395: 154:, and then rotating them in pairs about the three axes that pass through the centres of two opposite cubic faces. Each 527: 501: 139: 39: 190: 532: 494: 388: 208: 442: 422: 8: 100: 426: 446: 450: 122: 430: 186: 178: 159: 155: 151: 438: 478: 95: 434: 158:
is rotated by an equal (and opposite, within a pair) angle θ. Equivalently, a
521: 143: 61: 474: 147: 150:. It can be constructed by superimposing six identical copies of the 72: 28: 115: 413:
Skilling, John (1976), "Uniform Compounds of Uniform Polyhedra",
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Mathematical Proceedings of the Cambridge Philosophical Society
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Compound of twelve tetrahedra with rotational freedom (40°).stl
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Compound of twelve tetrahedra with rotational freedom (35°).stl
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Compound of twelve tetrahedra with rotational freedom (30°).stl
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Compound of twelve tetrahedra with rotational freedom (25°).stl
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Compound of twelve tetrahedra with rotational freedom (20°).stl
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Compound of twelve tetrahedra with rotational freedom (15°).stl
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Compound of twelve tetrahedra with rotational freedom (10°).stl
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Compound of twelve tetrahedra with rotational freedom (5°).stl
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coincide in pairs yielding (two superimposed copies of) the
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Compounds of twelve tetrahedra with rotational freedom
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Compound of twelve tetrahedra with rotational freedom
170:, which has the same vertices as this compound. 519: 502: 168:compound of six cubes with rotational freedom 21: 509: 495: 18: 412: 26: 520: 461: 13: 14: 544: 142:is a symmetric arrangement of 12 465: 386: 366: 346: 326: 306: 286: 266: 246: 226: 206: 27: 387: 367: 347: 327: 307: 287: 267: 247: 227: 216:Stellated octahedron (full).stl 207: 114: 94: 86: 78: 67: 56: 45: 35: 396:Compound of six tetrahedra.stl 118:restricting to one constituent 1: 406: 162:may be inscribed within each 481:. You can help Knowledge by 7: 140:uniform polyhedron compound 10: 549: 460: 196: 191:compound of six tetrahedra 435:10.1017/S0305004100052440 477:-related article is a 528:Polyhedral compounds 427:1976MPCPS..79..447S 185:is 45 degrees, the 16:Polyhedral compound 490: 489: 136: 135: 123:improper rotation 540: 533:Polyhedron stubs 511: 504: 497: 469: 462: 453: 392: 391: 372: 371: 352: 351: 332: 331: 312: 311: 292: 291: 272: 271: 252: 251: 232: 231: 212: 211: 187:stella octangula 179:stella octangula 160:stella octangula 156:stella octangula 152:stella octangula 146:, considered as 40:Uniform compound 31: 19: 548: 547: 543: 542: 541: 539: 538: 537: 518: 517: 516: 515: 458: 409: 402: 393: 382: 373: 362: 353: 342: 333: 322: 313: 302: 293: 282: 273: 262: 253: 242: 233: 222: 213: 199: 181:coincide. When 131: 109: 52: 17: 12: 11: 5: 546: 536: 535: 530: 514: 513: 506: 499: 491: 488: 487: 470: 456: 455: 421:(3): 447–457, 408: 405: 404: 403: 394: 385: 383: 374: 365: 363: 354: 345: 343: 334: 325: 323: 314: 305: 303: 294: 285: 283: 274: 265: 263: 254: 245: 243: 234: 225: 223: 214: 205: 203: 198: 195: 134: 133: 129: 119: 112: 111: 107: 98: 96:Symmetry group 92: 91: 88: 84: 83: 80: 76: 75: 69: 65: 64: 58: 54: 53: 50: 47: 43: 42: 37: 33: 32: 24: 23: 15: 9: 6: 4: 3: 2: 545: 534: 531: 529: 526: 525: 523: 512: 507: 505: 500: 498: 493: 492: 486: 484: 480: 476: 471: 468: 464: 463: 459: 452: 448: 444: 440: 436: 432: 428: 424: 420: 416: 411: 410: 400: 397: 390: 384: 380: 377: 370: 364: 360: 357: 350: 344: 340: 337: 330: 324: 320: 317: 310: 304: 300: 297: 290: 284: 280: 277: 270: 264: 260: 257: 250: 244: 240: 237: 230: 224: 220: 217: 210: 204: 201: 200: 194: 192: 188: 184: 180: 177:= 0, all six 176: 171: 169: 165: 161: 157: 153: 149: 145: 141: 128: 124: 120: 117: 113: 106: 102: 99: 97: 93: 89: 85: 81: 77: 74: 70: 66: 63: 59: 55: 48: 44: 41: 38: 34: 30: 25: 20: 483:expanding it 472: 457: 418: 414: 398: 378: 358: 338: 318: 298: 278: 258: 238: 218: 182: 174: 172: 137: 126: 104: 522:Categories 475:polyhedron 407:References 148:antiprisms 144:tetrahedra 101:octahedral 62:tetrahedra 451:123279687 73:triangles 57:Polyhedra 116:Subgroup 87:Vertices 443:0397554 423:Bibcode 197:Gallery 166:in the 121:4-fold 449:  441:  473:This 447:S2CID 401:= 45° 381:= 40° 361:= 35° 341:= 30° 321:= 25° 301:= 20° 281:= 15° 261:= 10° 173:When 138:This 79:Edges 68:Faces 46:Index 479:stub 241:= 5° 221:= 0° 164:cube 36:Type 431:doi 90:48 82:72 71:48 60:12 524:: 445:, 439:MR 437:, 429:, 419:79 417:, 193:. 132:) 110:) 49:UC 510:e 503:t 496:v 485:. 454:. 433:: 425:: 399:θ 379:θ 359:θ 339:θ 319:θ 299:θ 279:θ 259:θ 239:θ 219:θ 183:θ 175:θ 130:4 127:S 125:( 108:h 105:O 103:( 51:2

Index


Uniform compound
tetrahedra
triangles
Symmetry group
octahedral
Subgroup
improper rotation
uniform polyhedron compound
tetrahedra
antiprisms
stella octangula
stella octangula
stella octangula
cube
compound of six cubes with rotational freedom
stella octangula
stella octangula
compound of six tetrahedra
θ = 0°
Stellated octahedron (full).stl
θ = 5°
Compound of twelve tetrahedra with rotational freedom (5°).stl
θ = 10°
Compound of twelve tetrahedra with rotational freedom (10°).stl
θ = 15°
Compound of twelve tetrahedra with rotational freedom (15°).stl
θ = 20°
Compound of twelve tetrahedra with rotational freedom (20°).stl
θ = 25°

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