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Order-7 heptagrammic tiling

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of each heptagram around its points is one, and the winding number around the central heptagon is two, so adding these two numbers together, each point of the plane is surrounded three times; that is, the
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Each point of the hyperbolic plane that does not lie on a heptagram edge belongs to the central heptagon of one heptagram, and is in one of the points of exactly one other heptagram. The
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In the Euclidean plane, a heptagram of type {7/2} would have angles of 3
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of {7/2,7}. The heptagrams forming the tiling are of type {7/2},
411: 864: 714: 614: 510: 472: 468: 18: 318:, {3,7}. The full set of edges coincide with the edges of a 1585: 392:"Chapter 10: Regular honeycombs in hyperbolic space". 388:(Chapter 19, The Hyperbolic Archimedean Tessellations) 88: 1020: 947: 916: 878: 46:but its sources remain unclear because it lacks 1605: 484: 8: 1612: 1598: 875: 861: 711: 611: 507: 491: 477: 469: 802:Dividing a square into similar rectangles 77:Learn how and when to remove this message 376:, Heidi Burgiel, Chaim Goodman-Strauss, 355:-3 regular star-tiling on the sphere: 394:The Beauty of Geometry: Twelve Essays 351:, {5/2,5}, which is polyhedron and a 7: 1566: 1564: 216:Heptagrammic-order heptagonal tiling 1584:. You can help Knowledge (XXG) by 14: 1568: 601: 594: 359: 335: 330: 274: 190: 185: 180: 175: 170: 165: 160: 97: 23: 16:Tiling of the hyperbolic plane 1: 827:Regular Division of the Plane 326:one caused by crossed edges. 396:. Dover Publications. 1999. 349:small stellated dodecahedron 92:Order-7 heptagrammic tiling 735:Architectonic and catoptric 633:Aperiodic set of prototiles 247:order-7 heptagrammic tiling 1677: 1563: 455:"PoincarĂ© hyperbolic disk" 320:heptakis heptagonal tiling 874: 860: 721: 710: 623: 610: 592: 519: 506: 345:Kepler-Poinsot polyhedron 316:order-7 triangular tiling 291:of the tiling is 3. 118:Hyperbolic regular tiling 96: 91: 378:The Symmetries of Things 32:This article includes a 61:more precise citations. 1580:-related article is a 1661:Metric geometry stubs 269:star-tiling, and has 1651:Heptagrammic tilings 125:Vertex configuration 1578:hyperbolic geometry 436:"Hyperbolic tiling" 343:It is related to a 249:is a tiling of the 104:PoincarĂ© disk model 1631:Hyperbolic tilings 452:Weisstein, Eric W. 433:Weisstein, Eric W. 312:vertex arrangement 34:list of references 1641:Isohedral tilings 1593: 1592: 1558: 1557: 1554: 1553: 1550: 1549: 856: 855: 747:Computer graphics 706: 705: 590: 589: 386:978-1-56881-220-5 265:This tiling is a 239: 238: 226:Vertex-transitive 87: 86: 79: 1668: 1636:Isogonal tilings 1614: 1607: 1600: 1572: 1565: 876: 862: 814:Conway criterion 741:Circle Limit III 712: 645:Einstein problem 612: 605: 598: 534:Schwarz triangle 508: 493: 486: 479: 470: 465: 464: 446: 445: 415: 363: 339: 334: 310:It has the same 301: 297: 278: 251:hyperbolic plane 195: 194: 193: 189: 188: 184: 183: 179: 178: 174: 173: 169: 168: 164: 163: 108:hyperbolic plane 101: 89: 82: 75: 71: 68: 62: 57:this article by 48:inline citations 27: 26: 19: 1676: 1675: 1671: 1670: 1669: 1667: 1666: 1665: 1656:Order-7 tilings 1646:Regular tilings 1621: 1620: 1619: 1618: 1561: 1559: 1546: 1023: 1016: 949: 943: 912: 870: 852: 717: 702: 619: 606: 600: 599: 586: 577:Wallpaper group 515: 502: 497: 450: 449: 431: 430: 427: 422: 404: 391: 370: 314:as the regular 308: 306:Related tilings 299: 295: 271:SchlĂ€fli symbol 263: 253:by overlapping 234:face-transitive 230:edge-transitive 191: 186: 181: 176: 171: 166: 161: 159: 155:Coxeter diagram 149:7 | 7/2 2 135:SchlĂ€fli symbol 102: 83: 72: 66: 63: 52: 38:related reading 28: 24: 17: 12: 11: 5: 1674: 1672: 1664: 1663: 1658: 1653: 1648: 1643: 1638: 1633: 1623: 1622: 1617: 1616: 1609: 1602: 1594: 1591: 1590: 1573: 1556: 1555: 1552: 1551: 1548: 1547: 1545: 1544: 1539: 1534: 1529: 1524: 1519: 1514: 1509: 1504: 1499: 1494: 1489: 1484: 1479: 1474: 1469: 1464: 1459: 1454: 1449: 1444: 1439: 1434: 1429: 1424: 1419: 1414: 1409: 1404: 1399: 1394: 1389: 1384: 1379: 1374: 1369: 1364: 1359: 1354: 1349: 1344: 1339: 1334: 1329: 1324: 1319: 1314: 1309: 1304: 1299: 1294: 1289: 1284: 1279: 1274: 1269: 1264: 1259: 1254: 1249: 1244: 1239: 1234: 1229: 1224: 1219: 1214: 1209: 1204: 1199: 1194: 1189: 1184: 1179: 1174: 1169: 1164: 1159: 1154: 1149: 1144: 1139: 1134: 1129: 1124: 1119: 1114: 1109: 1104: 1099: 1094: 1089: 1084: 1079: 1074: 1069: 1064: 1059: 1054: 1049: 1044: 1039: 1034: 1028: 1026: 1018: 1017: 1015: 1014: 1009: 1004: 999: 994: 989: 984: 979: 974: 969: 964: 959: 953: 951: 945: 944: 942: 941: 936: 931: 926: 920: 918: 914: 913: 911: 910: 905: 900: 895: 890: 884: 882: 872: 871: 865: 858: 857: 854: 853: 851: 850: 845: 840: 835: 830: 823: 822: 821: 816: 806: 805: 804: 799: 794: 789: 788: 787: 774: 769: 764: 759: 754: 749: 744: 737: 732: 722: 719: 718: 715: 708: 707: 704: 703: 701: 700: 695: 690: 689: 688: 674: 669: 664: 659: 654: 653: 652: 650:Socolar–Taylor 642: 641: 640: 630: 628:Ammann–Beenker 624: 621: 620: 615: 608: 607: 593: 591: 588: 587: 585: 584: 579: 574: 573: 572: 567: 562: 551:Uniform tiling 548: 547: 546: 536: 531: 526: 520: 517: 516: 511: 504: 503: 498: 496: 495: 488: 481: 473: 467: 466: 447: 426: 425:External links 423: 421: 418: 417: 416: 402: 389: 374:John H. Conway 369: 366: 365: 364: 341: 340: 307: 304: 284:winding number 262: 259: 237: 236: 223: 219: 218: 213: 207: 206: 203: 201:Symmetry group 197: 196: 157: 151: 150: 147: 145:Wythoff symbol 141: 140: 137: 131: 130: 127: 121: 120: 115: 111: 110: 94: 93: 85: 84: 42:external links 31: 29: 22: 15: 13: 10: 9: 6: 4: 3: 2: 1673: 1662: 1659: 1657: 1654: 1652: 1649: 1647: 1644: 1642: 1639: 1637: 1634: 1632: 1629: 1628: 1626: 1615: 1610: 1608: 1603: 1601: 1596: 1595: 1589: 1587: 1583: 1579: 1574: 1571: 1567: 1562: 1543: 1540: 1538: 1535: 1533: 1530: 1528: 1525: 1523: 1520: 1518: 1515: 1513: 1510: 1508: 1505: 1503: 1500: 1498: 1495: 1493: 1490: 1488: 1485: 1483: 1480: 1478: 1475: 1473: 1470: 1468: 1465: 1463: 1460: 1458: 1455: 1453: 1450: 1448: 1445: 1443: 1440: 1438: 1435: 1433: 1430: 1428: 1425: 1423: 1420: 1418: 1415: 1413: 1410: 1408: 1405: 1403: 1400: 1398: 1395: 1393: 1390: 1388: 1385: 1383: 1380: 1378: 1375: 1373: 1370: 1368: 1365: 1363: 1360: 1358: 1355: 1353: 1350: 1348: 1345: 1343: 1340: 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139:{7/2,7} 1422:6.4.8.4 1377:5.4.6.4 1337:4.12.16 1327:4.10.12 1297:V4.8.10 1272:V4.6.16 1262:V4.6.14 1162:3.6.4.6 1157:3.4.∞.4 1152:3.4.8.4 1147:3.4.7.4 1142:3.4.6.4 1092:3.∞.3.∞ 1087:3.4.3.4 1082:3.8.3.8 1077:3.7.3.7 1072:3.6.3.8 1067:3.6.3.6 1062:3.5.3.6 1057:3.5.3.5 1052:3.4.3.∞ 1047:3.4.3.8 1042:3.4.3.7 1037:3.4.3.6 1032:3.4.3.5 987:3.4.6.4 957:3.4.3.4 950:regular 917:Regular 843:Voronoi 767:Packing 698:Truchet 693:Socolar 662:Penrose 657:Gilbert 582:Wythoff 353:density 289:density 267:regular 106:of the 55:improve 1312:4.8.16 1307:4.8.14 1302:4.8.12 1292:4.8.10 1267:4.6.16 1257:4.6.14 1252:4.6.12 1022:Hyper- 1007:4.6.12 780:Domino 686:Sphinx 565:Convex 544:Domino 410:  400:  384:  380:2008, 347:, the 245:, the 129:(7/2) 1576:This 1427:(6.8) 1382:(5.6) 1317:4.8.∞ 1287:(4.8) 1282:(4.7) 1277:4.6.∞ 1247:(4.6) 1242:(4.5) 1212:4.∞.4 1207:4.8.4 1202:4.7.4 1197:4.6.4 1192:4.5.4 1172:(3.8) 1167:(3.7) 1137:(3.4) 1132:(3.4) 1024:bolic 992:(3.6) 948:Semi- 819:Girih 716:Other 40:, or 1582:stub 1512:8.16 1507:8.12 1477:7.14 1447:6.16 1442:6.12 1437:6.10 1397:5.12 1392:5.10 1347:4.16 1342:4.14 1332:4.12 1322:4.10 1182:3.16 1177:3.14 997:3.12 982:V3.6 908:V4.n 898:V3.n 785:Wang 762:List 728:and 679:and 638:List 553:and 408:LCCN 398:ISBN 382:ISBN 211:Dual 114:Type 1542:∞.8 1537:∞.6 1502:8.6 1472:7.8 1467:7.6 1432:6.8 1387:5.8 1352:4.∞ 1187:3.∞ 1112:3.4 1107:3.∞ 1102:3.8 1097:3.7 1012:4.8 1002:4.∞ 977:3.6 972:3.∞ 967:3.4 903:4.n 893:3.n 866:By 241:In 1627:: 457:. 438:. 406:. 257:. 232:, 228:, 44:, 36:, 1613:e 1606:t 1599:v 1588:. 1532:∞ 1527:∞ 1522:∞ 1517:∞ 1497:8 1492:8 1487:8 1482:8 1462:7 1457:7 1452:7 1417:6 1412:6 1407:6 1402:6 1372:5 1367:5 1362:5 1357:5 1237:4 1232:4 1227:4 1222:4 1217:4 1127:3 1122:3 1117:3 939:6 934:4 929:3 924:2 888:2 492:e 485:t 478:v 463:. 444:. 414:. 300:π 296:π 80:) 74:( 69:) 65:( 51:.

Index

list of references
related reading
external links
inline citations
improve
introducing
Learn how and when to remove this message
Order-7 heptagrammic tiling
Poincaré disk model
hyperbolic plane
Hyperbolic regular tiling
Vertex configuration
SchlÀfli symbol
Wythoff symbol
Coxeter diagram
Symmetry group
Dual
Heptagrammic-order heptagonal tiling
Vertex-transitive
edge-transitive
face-transitive
geometry
hyperbolic plane
heptagrams
regular
SchlÀfli symbol

winding number
density
vertex arrangement

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