Knowledge (XXG)

Icosahedral number

Source đź“ť

2486: 2510: 96: 588: 223: 109: 581: 156:
was lost, and not rediscovered until 1860. In the meantime, icosahedral numbers had been studied again by other mathematicians, including
1388: 574: 2551: 1383: 165: 1398: 1378: 2091: 1671: 1393: 216: 2177: 1493: 1843: 1162: 955: 401: 1878: 1848: 1523: 1513: 2019: 1433: 1167: 1147: 406: 386: 1709: 1873: 1968: 1591: 1348: 1157: 1139: 1033: 1023: 1013: 396: 378: 277: 267: 257: 1853: 2570: 2096: 1641: 1262: 1048: 1043: 1038: 1028: 1005: 501: 292: 287: 282: 272: 249: 209: 157: 1081: 185: 1338: 38: 2207: 2172: 1958: 1868: 1742: 1717: 1626: 1616: 1228: 1210: 1130: 467: 444: 369: 2544: 2467: 1737: 1611: 1242: 1018: 798: 725: 481: 262: 189: 149: 102:
The first such numbers are 1, 12, 48, 124, 255, 456, 742, 1128, 1629, 2260, 3036, 3972, 5083, … (sequence
2575: 1722: 1576: 1503: 658: 536: 2431: 2071: 161: 2364: 2258: 2222: 1963: 1686: 1666: 1483: 1152: 940: 912: 391: 2086: 1950: 1945: 1913: 1676: 1651: 1646: 1621: 1551: 1547: 1478: 1368: 1200: 996: 965: 434: 240: 2485: 2489: 2243: 2238: 2152: 2126: 2024: 2003: 1775: 1656: 1606: 1528: 1498: 1438: 1185: 1116: 829: 462: 355: 194:, Sources in the History of Mathematics and Physical Sciences, vol. 4, Springer, p. 118 1373: 2537: 2383: 2328: 2182: 2157: 2131: 1908: 1586: 1581: 1508: 1488: 1473: 1195: 1177: 1096: 1086: 1071: 849: 834: 429: 416: 335: 325: 315: 121: 2521: 2419: 2212: 1798: 1770: 1760: 1752: 1636: 1601: 1596: 1563: 1257: 1220: 1111: 1106: 1101: 1091: 1063: 950: 902: 897: 854: 793: 496: 454: 350: 345: 340: 330: 307: 137: 133: 129: 2395: 2284: 2217: 2143: 2066: 2040: 1858: 1571: 1428: 1363: 1333: 1323: 1318: 984: 892: 839: 683: 623: 232: 21: 2400: 2268: 2253: 2117: 2081: 2056: 1932: 1903: 1888: 1765: 1661: 1631: 1358: 1313: 1190: 788: 783: 778: 750: 735: 648: 633: 611: 598: 424: 145: 141: 2564: 2323: 2307: 2248: 2202: 1898: 1883: 1793: 1518: 1076: 945: 907: 864: 745: 730: 720: 678: 668: 643: 546: 320: 128:. Prior to Descartes, figurate numbers had been studied by the ancient Greeks and by 2359: 2348: 2263: 2101: 2076: 1993: 1893: 1863: 1838: 1822: 1727: 1694: 1443: 1417: 1328: 1267: 844: 740: 673: 653: 628: 551: 506: 2318: 2193: 1998: 1462: 1353: 1308: 1303: 1053: 960: 859: 688: 663: 638: 541: 297: 25: 2455: 2436: 1732: 1343: 566: 2061: 1988: 1980: 1785: 1699: 817: 521: 2162: 2167: 1826: 2517: 2509: 201: 144:. Descartes introduced the study of figurate numbers based on the 2453: 2417: 2381: 2345: 2305: 1930: 1819: 1545: 1460: 1415: 1292: 982: 929: 881: 815: 767: 705: 609: 570: 205: 191:
Descartes on Polyhedra: A Study of the "De solidorum elementis"
120:
The first study of icosahedral numbers appears to have been by
104: 2525: 152:; his work included the icosahedral numbers. However, 41: 2277: 2231: 2191: 2142: 2116: 2049: 2033: 2012: 1979: 1944: 1784: 1751: 1708: 1685: 1562: 1250: 1241: 1219: 1176: 1138: 1129: 1062: 1004: 995: 529: 519: 489: 480: 453: 415: 377: 368: 306: 248: 239: 90: 32:th icosahedral number is given by the formula 2545: 582: 217: 8: 2552: 2538: 2450: 2414: 2378: 2342: 2302: 1976: 1941: 1927: 1816: 1559: 1542: 1457: 1412: 1289: 1247: 1135: 1001: 992: 979: 926: 883:Possessing a specific set of other numbers 878: 812: 764: 702: 606: 589: 575: 567: 526: 486: 374: 245: 224: 210: 202: 58: 42: 40: 91:{\displaystyle {n(5n^{2}-5n+2) \over 2}} 177: 7: 2506: 2504: 2524:. You can help Knowledge (XXG) by 14: 2508: 2484: 2092:Perfect digit-to-digit invariant 79: 48: 1: 931:Expressible via specific sums 402:Centered dodecahedral numbers 407:Centered icosahedral numbers 387:Centered tetrahedral numbers 2020:Multiplicative digital root 397:Centered octahedral numbers 278:Centered heptagonal numbers 268:Centered pentagonal numbers 258:Centered triangular numbers 2592: 2503: 502:Squared triangular numbers 293:Centered decagonal numbers 288:Centered nonagonal numbers 283:Centered octagonal numbers 273:Centered hexagonal numbers 2480: 2463: 2449: 2427: 2413: 2391: 2377: 2355: 2341: 2314: 2301: 2097:Perfect digital invariant 1940: 1926: 1834: 1815: 1672:Superior highly composite 1558: 1541: 1469: 1456: 1424: 1411: 1299: 1288: 991: 978: 936: 925: 888: 877: 825: 811: 774: 763: 716: 701: 619: 605: 186:Federico, Pasquale Joseph 158:Friedrich Wilhelm Marpurg 1710:Euler's totient function 1494:Euler–Jacobi pseudoprime 769:Other polynomial numbers 468:Square pyramidal numbers 445:Stella octangula numbers 1524:Somer–Lucas pseudoprime 1514:Lucas–Carmichael number 1349:Lazy caterer's sequence 263:Centered square numbers 1399:Wedderburn–Etherington 799:Lucky numbers of Euler 154:De solidorum elementis 126:De solidorum elementis 124:, around 1630, in his 92: 2516:This article about a 1687:Prime omega functions 1504:Frobenius pseudoprime 1294:Combinatorial numbers 1163:Centered dodecahedral 956:Primary pseudoperfect 392:Centered cube numbers 166:Sir Frederick Pollock 150:semiregular polyhedra 93: 2146:-composition related 1946:Arithmetic functions 1548:Arithmetic functions 1484:Elliptic pseudoprime 1168:Centered icosahedral 1148:Centered tetrahedral 435:Dodecahedral numbers 39: 2072:Kaprekar's constant 1592:Colossally abundant 1479:Catalan pseudoprime 1379:Schröder–Hipparchus 1158:Centered octahedral 1034:Centered heptagonal 1024:Centered pentagonal 1014:Centered triangular 614:and related numbers 552:8-hypercube numbers 547:7-hypercube numbers 542:6-hypercube numbers 537:5-hypercube numbers 507:Tesseractic numbers 463:Tetrahedral numbers 440:Icosahedral numbers 356:Dodecagonal numbers 24:that represents an 2490:Mathematics portal 2432:Aronson's sequence 2178:Smarandache–Wellin 1935:-dependent numbers 1642:Primitive abundant 1529:Strong pseudoprime 1519:Perrin pseudoprime 1499:Fermat pseudoprime 1439:Wolstenholme prime 1263:Squared triangular 1049:Centered decagonal 1044:Centered nonagonal 1039:Centered octagonal 1029:Centered hexagonal 430:Octahedral numbers 336:Heptagonal numbers 326:Pentagonal numbers 316:Triangular numbers 162:Georg Simon KlĂĽgel 88: 18:icosahedral number 2533: 2532: 2498: 2497: 2476: 2475: 2445: 2444: 2409: 2408: 2373: 2372: 2337: 2336: 2297: 2296: 2293: 2292: 2112: 2111: 1922: 1921: 1811: 1810: 1807: 1806: 1753:Aliquot sequences 1564:Divisor functions 1537: 1536: 1509:Lucas pseudoprime 1489:Euler pseudoprime 1474:Carmichael number 1452: 1451: 1407: 1406: 1284: 1283: 1280: 1279: 1276: 1275: 1237: 1236: 1125: 1124: 1082:Square triangular 974: 973: 921: 920: 873: 872: 807: 806: 759: 758: 697: 696: 564: 563: 560: 559: 515: 514: 497:Pentatope numbers 476: 475: 364: 363: 351:Decagonal numbers 346:Nonagonal numbers 341:Octagonal numbers 331:Hexagonal numbers 138:pyramidal numbers 134:polygonal numbers 86: 2583: 2571:Figurate numbers 2554: 2547: 2540: 2512: 2505: 2488: 2451: 2420:Natural language 2415: 2379: 2347:Generated via a 2343: 2303: 2208:Digit-reassembly 2173:Self-descriptive 1977: 1942: 1928: 1879:Lucas–Carmichael 1869:Harmonic divisor 1817: 1743:Sparsely totient 1718:Highly cototient 1627:Multiply perfect 1617:Highly composite 1560: 1543: 1458: 1413: 1394:Telephone number 1290: 1248: 1229:Square pyramidal 1211:Stella octangula 1136: 1002: 993: 985:Figurate numbers 980: 927: 879: 813: 765: 703: 607: 591: 584: 577: 568: 527: 487: 375: 246: 233:Figurate numbers 226: 219: 212: 203: 196: 195: 182: 130:Johann Faulhaber 107: 97: 95: 94: 89: 87: 82: 63: 62: 43: 2591: 2590: 2586: 2585: 2584: 2582: 2581: 2580: 2561: 2560: 2559: 2558: 2501: 2499: 2494: 2472: 2468:Strobogrammatic 2459: 2441: 2423: 2405: 2387: 2369: 2351: 2333: 2310: 2289: 2273: 2232:Divisor-related 2227: 2187: 2138: 2108: 2045: 2029: 2008: 1975: 1948: 1936: 1918: 1830: 1829:related numbers 1803: 1780: 1747: 1738:Perfect totient 1704: 1681: 1612:Highly abundant 1554: 1533: 1465: 1448: 1420: 1403: 1389:Stirling second 1295: 1272: 1233: 1215: 1172: 1121: 1058: 1019:Centered square 987: 970: 932: 917: 884: 869: 821: 820:defined numbers 803: 770: 755: 726:Double Mersenne 712: 693: 615: 601: 599:natural numbers 595: 565: 556: 511: 472: 449: 411: 360: 302: 235: 230: 200: 199: 184: 183: 179: 174: 146:Platonic solids 132:, but only for 118: 103: 54: 44: 37: 36: 22:figurate number 12: 11: 5: 2589: 2587: 2579: 2578: 2573: 2563: 2562: 2557: 2556: 2549: 2542: 2534: 2531: 2530: 2513: 2496: 2495: 2493: 2492: 2481: 2478: 2477: 2474: 2473: 2471: 2470: 2464: 2461: 2460: 2454: 2447: 2446: 2443: 2442: 2440: 2439: 2434: 2428: 2425: 2424: 2418: 2411: 2410: 2407: 2406: 2404: 2403: 2401:Sorting number 2398: 2396:Pancake number 2392: 2389: 2388: 2382: 2375: 2374: 2371: 2370: 2368: 2367: 2362: 2356: 2353: 2352: 2346: 2339: 2338: 2335: 2334: 2332: 2331: 2326: 2321: 2315: 2312: 2311: 2308:Binary numbers 2306: 2299: 2298: 2295: 2294: 2291: 2290: 2288: 2287: 2281: 2279: 2275: 2274: 2272: 2271: 2266: 2261: 2256: 2251: 2246: 2241: 2235: 2233: 2229: 2228: 2226: 2225: 2220: 2215: 2210: 2205: 2199: 2197: 2189: 2188: 2186: 2185: 2180: 2175: 2170: 2165: 2160: 2155: 2149: 2147: 2140: 2139: 2137: 2136: 2135: 2134: 2123: 2121: 2118:P-adic numbers 2114: 2113: 2110: 2109: 2107: 2106: 2105: 2104: 2094: 2089: 2084: 2079: 2074: 2069: 2064: 2059: 2053: 2051: 2047: 2046: 2044: 2043: 2037: 2035: 2034:Coding-related 2031: 2030: 2028: 2027: 2022: 2016: 2014: 2010: 2009: 2007: 2006: 2001: 1996: 1991: 1985: 1983: 1974: 1973: 1972: 1971: 1969:Multiplicative 1966: 1955: 1953: 1938: 1937: 1933:Numeral system 1931: 1924: 1923: 1920: 1919: 1917: 1916: 1911: 1906: 1901: 1896: 1891: 1886: 1881: 1876: 1871: 1866: 1861: 1856: 1851: 1846: 1841: 1835: 1832: 1831: 1820: 1813: 1812: 1809: 1808: 1805: 1804: 1802: 1801: 1796: 1790: 1788: 1782: 1781: 1779: 1778: 1773: 1768: 1763: 1757: 1755: 1749: 1748: 1746: 1745: 1740: 1735: 1730: 1725: 1723:Highly totient 1720: 1714: 1712: 1706: 1705: 1703: 1702: 1697: 1691: 1689: 1683: 1682: 1680: 1679: 1674: 1669: 1664: 1659: 1654: 1649: 1644: 1639: 1634: 1629: 1624: 1619: 1614: 1609: 1604: 1599: 1594: 1589: 1584: 1579: 1577:Almost perfect 1574: 1568: 1566: 1556: 1555: 1546: 1539: 1538: 1535: 1534: 1532: 1531: 1526: 1521: 1516: 1511: 1506: 1501: 1496: 1491: 1486: 1481: 1476: 1470: 1467: 1466: 1461: 1454: 1453: 1450: 1449: 1447: 1446: 1441: 1436: 1431: 1425: 1422: 1421: 1416: 1409: 1408: 1405: 1404: 1402: 1401: 1396: 1391: 1386: 1384:Stirling first 1381: 1376: 1371: 1366: 1361: 1356: 1351: 1346: 1341: 1336: 1331: 1326: 1321: 1316: 1311: 1306: 1300: 1297: 1296: 1293: 1286: 1285: 1282: 1281: 1278: 1277: 1274: 1273: 1271: 1270: 1265: 1260: 1254: 1252: 1245: 1239: 1238: 1235: 1234: 1232: 1231: 1225: 1223: 1217: 1216: 1214: 1213: 1208: 1203: 1198: 1193: 1188: 1182: 1180: 1174: 1173: 1171: 1170: 1165: 1160: 1155: 1150: 1144: 1142: 1133: 1127: 1126: 1123: 1122: 1120: 1119: 1114: 1109: 1104: 1099: 1094: 1089: 1084: 1079: 1074: 1068: 1066: 1060: 1059: 1057: 1056: 1051: 1046: 1041: 1036: 1031: 1026: 1021: 1016: 1010: 1008: 999: 989: 988: 983: 976: 975: 972: 971: 969: 968: 963: 958: 953: 948: 943: 937: 934: 933: 930: 923: 922: 919: 918: 916: 915: 910: 905: 900: 895: 889: 886: 885: 882: 875: 874: 871: 870: 868: 867: 862: 857: 852: 847: 842: 837: 832: 826: 823: 822: 816: 809: 808: 805: 804: 802: 801: 796: 791: 786: 781: 775: 772: 771: 768: 761: 760: 757: 756: 754: 753: 748: 743: 738: 733: 728: 723: 717: 714: 713: 706: 699: 698: 695: 694: 692: 691: 686: 681: 676: 671: 666: 661: 656: 651: 646: 641: 636: 631: 626: 620: 617: 616: 610: 603: 602: 596: 594: 593: 586: 579: 571: 562: 561: 558: 557: 555: 554: 549: 544: 539: 533: 531: 524: 517: 516: 513: 512: 510: 509: 504: 499: 493: 491: 484: 478: 477: 474: 473: 471: 470: 465: 459: 457: 451: 450: 448: 447: 442: 437: 432: 427: 421: 419: 413: 412: 410: 409: 404: 399: 394: 389: 383: 381: 372: 366: 365: 362: 361: 359: 358: 353: 348: 343: 338: 333: 328: 323: 321:Square numbers 318: 312: 310: 304: 303: 301: 300: 295: 290: 285: 280: 275: 270: 265: 260: 254: 252: 243: 237: 236: 231: 229: 228: 221: 214: 206: 198: 197: 176: 175: 173: 170: 122:RenĂ© Descartes 117: 114: 100: 99: 85: 81: 78: 75: 72: 69: 66: 61: 57: 53: 50: 47: 13: 10: 9: 6: 4: 3: 2: 2588: 2577: 2574: 2572: 2569: 2568: 2566: 2555: 2550: 2548: 2543: 2541: 2536: 2535: 2529: 2527: 2523: 2519: 2514: 2511: 2507: 2502: 2491: 2487: 2483: 2482: 2479: 2469: 2466: 2465: 2462: 2457: 2452: 2448: 2438: 2435: 2433: 2430: 2429: 2426: 2421: 2416: 2412: 2402: 2399: 2397: 2394: 2393: 2390: 2385: 2380: 2376: 2366: 2363: 2361: 2358: 2357: 2354: 2350: 2344: 2340: 2330: 2327: 2325: 2322: 2320: 2317: 2316: 2313: 2309: 2304: 2300: 2286: 2283: 2282: 2280: 2276: 2270: 2267: 2265: 2262: 2260: 2259:Polydivisible 2257: 2255: 2252: 2250: 2247: 2245: 2242: 2240: 2237: 2236: 2234: 2230: 2224: 2221: 2219: 2216: 2214: 2211: 2209: 2206: 2204: 2201: 2200: 2198: 2195: 2190: 2184: 2181: 2179: 2176: 2174: 2171: 2169: 2166: 2164: 2161: 2159: 2156: 2154: 2151: 2150: 2148: 2145: 2141: 2133: 2130: 2129: 2128: 2125: 2124: 2122: 2119: 2115: 2103: 2100: 2099: 2098: 2095: 2093: 2090: 2088: 2085: 2083: 2080: 2078: 2075: 2073: 2070: 2068: 2065: 2063: 2060: 2058: 2055: 2054: 2052: 2048: 2042: 2039: 2038: 2036: 2032: 2026: 2023: 2021: 2018: 2017: 2015: 2013:Digit product 2011: 2005: 2002: 2000: 1997: 1995: 1992: 1990: 1987: 1986: 1984: 1982: 1978: 1970: 1967: 1965: 1962: 1961: 1960: 1957: 1956: 1954: 1952: 1947: 1943: 1939: 1934: 1929: 1925: 1915: 1912: 1910: 1907: 1905: 1902: 1900: 1897: 1895: 1892: 1890: 1887: 1885: 1882: 1880: 1877: 1875: 1872: 1870: 1867: 1865: 1862: 1860: 1857: 1855: 1852: 1850: 1849:ErdĹ‘s–Nicolas 1847: 1845: 1842: 1840: 1837: 1836: 1833: 1828: 1824: 1818: 1814: 1800: 1797: 1795: 1792: 1791: 1789: 1787: 1783: 1777: 1774: 1772: 1769: 1767: 1764: 1762: 1759: 1758: 1756: 1754: 1750: 1744: 1741: 1739: 1736: 1734: 1731: 1729: 1726: 1724: 1721: 1719: 1716: 1715: 1713: 1711: 1707: 1701: 1698: 1696: 1693: 1692: 1690: 1688: 1684: 1678: 1675: 1673: 1670: 1668: 1667:Superabundant 1665: 1663: 1660: 1658: 1655: 1653: 1650: 1648: 1645: 1643: 1640: 1638: 1635: 1633: 1630: 1628: 1625: 1623: 1620: 1618: 1615: 1613: 1610: 1608: 1605: 1603: 1600: 1598: 1595: 1593: 1590: 1588: 1585: 1583: 1580: 1578: 1575: 1573: 1570: 1569: 1567: 1565: 1561: 1557: 1553: 1549: 1544: 1540: 1530: 1527: 1525: 1522: 1520: 1517: 1515: 1512: 1510: 1507: 1505: 1502: 1500: 1497: 1495: 1492: 1490: 1487: 1485: 1482: 1480: 1477: 1475: 1472: 1471: 1468: 1464: 1459: 1455: 1445: 1442: 1440: 1437: 1435: 1432: 1430: 1427: 1426: 1423: 1419: 1414: 1410: 1400: 1397: 1395: 1392: 1390: 1387: 1385: 1382: 1380: 1377: 1375: 1372: 1370: 1367: 1365: 1362: 1360: 1357: 1355: 1352: 1350: 1347: 1345: 1342: 1340: 1337: 1335: 1332: 1330: 1327: 1325: 1322: 1320: 1317: 1315: 1312: 1310: 1307: 1305: 1302: 1301: 1298: 1291: 1287: 1269: 1266: 1264: 1261: 1259: 1256: 1255: 1253: 1249: 1246: 1244: 1243:4-dimensional 1240: 1230: 1227: 1226: 1224: 1222: 1218: 1212: 1209: 1207: 1204: 1202: 1199: 1197: 1194: 1192: 1189: 1187: 1184: 1183: 1181: 1179: 1175: 1169: 1166: 1164: 1161: 1159: 1156: 1154: 1153:Centered cube 1151: 1149: 1146: 1145: 1143: 1141: 1137: 1134: 1132: 1131:3-dimensional 1128: 1118: 1115: 1113: 1110: 1108: 1105: 1103: 1100: 1098: 1095: 1093: 1090: 1088: 1085: 1083: 1080: 1078: 1075: 1073: 1070: 1069: 1067: 1065: 1061: 1055: 1052: 1050: 1047: 1045: 1042: 1040: 1037: 1035: 1032: 1030: 1027: 1025: 1022: 1020: 1017: 1015: 1012: 1011: 1009: 1007: 1003: 1000: 998: 997:2-dimensional 994: 990: 986: 981: 977: 967: 964: 962: 959: 957: 954: 952: 949: 947: 944: 942: 941:Nonhypotenuse 939: 938: 935: 928: 924: 914: 911: 909: 906: 904: 901: 899: 896: 894: 891: 890: 887: 880: 876: 866: 863: 861: 858: 856: 853: 851: 848: 846: 843: 841: 838: 836: 833: 831: 828: 827: 824: 819: 814: 810: 800: 797: 795: 792: 790: 787: 785: 782: 780: 777: 776: 773: 766: 762: 752: 749: 747: 744: 742: 739: 737: 734: 732: 729: 727: 724: 722: 719: 718: 715: 710: 704: 700: 690: 687: 685: 682: 680: 679:Perfect power 677: 675: 672: 670: 669:Seventh power 667: 665: 662: 660: 657: 655: 652: 650: 647: 645: 642: 640: 637: 635: 632: 630: 627: 625: 622: 621: 618: 613: 608: 604: 600: 592: 587: 585: 580: 578: 573: 572: 569: 553: 550: 548: 545: 543: 540: 538: 535: 534: 532: 528: 525: 523: 518: 508: 505: 503: 500: 498: 495: 494: 492: 488: 485: 483: 482:4-dimensional 479: 469: 466: 464: 461: 460: 458: 456: 452: 446: 443: 441: 438: 436: 433: 431: 428: 426: 423: 422: 420: 418: 414: 408: 405: 403: 400: 398: 395: 393: 390: 388: 385: 384: 382: 380: 376: 373: 371: 370:3-dimensional 367: 357: 354: 352: 349: 347: 344: 342: 339: 337: 334: 332: 329: 327: 324: 322: 319: 317: 314: 313: 311: 309: 305: 299: 296: 294: 291: 289: 286: 284: 281: 279: 276: 274: 271: 269: 266: 264: 261: 259: 256: 255: 253: 251: 247: 244: 242: 241:2-dimensional 238: 234: 227: 222: 220: 215: 213: 208: 207: 204: 193: 192: 187: 181: 178: 171: 169: 167: 164:in 1808, and 163: 159: 155: 151: 147: 143: 139: 135: 131: 127: 123: 115: 113: 111: 106: 83: 76: 73: 70: 67: 64: 59: 55: 51: 45: 35: 34: 33: 31: 27: 23: 19: 2576:Number stubs 2526:expanding it 2515: 2500: 2223:Transposable 2087:Narcissistic 1994:Digital root 1914:Super-Poulet 1874:Jordan–PĂłlya 1823:prime factor 1728:Noncototient 1695:Almost prime 1677:Superperfect 1652:Refactorable 1647:Quasiperfect 1622:Hyperperfect 1463:Pseudoprimes 1434:Wall–Sun–Sun 1369:Ordered Bell 1339:Fuss–Catalan 1251:non-centered 1205: 1201:Dodecahedral 1178:non-centered 1064:non-centered 966:Wolstenholme 711:× 2 ± 1 708: 707:Of the form 674:Eighth power 654:Fourth power 530:non-centered 490:non-centered 439: 425:Cube numbers 417:non-centered 308:non-centered 298:Star numbers 190: 180: 153: 125: 119: 101: 29: 17: 15: 2244:Extravagant 2239:Equidigital 2194:permutation 2153:Palindromic 2127:Automorphic 2025:Sum-product 2004:Sum-product 1959:Persistence 1854:ErdĹ‘s–Woods 1776:Untouchable 1657:Semiperfect 1607:Hemiperfect 1268:Tesseractic 1206:Icosahedral 1186:Tetrahedral 1117:Dodecagonal 818:Recursively 689:Prime power 664:Sixth power 659:Fifth power 639:Power of 10 597:Classes of 522:dimensional 26:icosahedron 2565:Categories 2456:Graphemics 2329:Pernicious 2183:Undulating 2158:Pandigital 2132:Trimorphic 1733:Nontotient 1582:Arithmetic 1196:Octahedral 1097:Heptagonal 1087:Pentagonal 1072:Triangular 913:SierpiĹ„ski 835:Jacobsthal 634:Power of 3 629:Power of 2 172:References 2213:Parasitic 2062:Factorion 1989:Digit sum 1981:Digit sum 1799:Fortunate 1786:Primorial 1700:Semiprime 1637:Practical 1602:Descartes 1597:Deficient 1587:Betrothed 1429:Wieferich 1258:Pentatope 1221:pyramidal 1112:Decagonal 1107:Nonagonal 1102:Octagonal 1092:Hexagonal 951:Practical 898:Congruent 830:Fibonacci 794:Loeschian 455:pyramidal 168:in 1850. 160:in 1774, 148:and some 65:− 2285:Friedman 2218:Primeval 2163:Repdigit 2120:-related 2067:Kaprekar 2041:Meertens 1964:Additive 1951:dynamics 1859:Friendly 1771:Sociable 1761:Amicable 1572:Abundant 1552:dynamics 1374:Schröder 1364:Narayana 1334:Eulerian 1324:Delannoy 1319:Dedekind 1140:centered 1006:centered 893:Amenable 850:Narayana 840:Leonardo 736:Mersenne 684:Powerful 624:Achilles 379:centered 250:centered 188:(1982), 2458:related 2422:related 2386:related 2384:Sorting 2269:Vampire 2254:Harshad 2196:related 2168:Repunit 2082:Lychrel 2057:Dudeney 1909:Størmer 1904:Sphenic 1889:Regular 1827:divisor 1766:Perfect 1662:Sublime 1632:Perfect 1359:Motzkin 1314:Catalan 855:Padovan 789:Leyland 784:Idoneal 779:Hilbert 751:Woodall 520:Higher 116:History 108:in the 105:A006564 2518:number 2324:Odious 2249:Frugal 2203:Cyclic 2192:Digit- 1899:Smooth 1884:Pronic 1844:Cyclic 1821:Other 1794:Euclid 1444:Wilson 1418:Primes 1077:Square 946:Polite 908:Riesel 903:Knödel 865:Perrin 746:Thabit 731:Fermat 721:Cullen 644:Square 612:Powers 140:, and 28:. The 2520:is a 2365:Prime 2360:Lucky 2349:sieve 2278:Other 2264:Smith 2144:Digit 2102:Happy 2077:Keith 2050:Other 1894:Rough 1864:Giuga 1329:Euler 1191:Cubic 845:Lucas 741:Proth 142:cubes 20:is a 2522:stub 2319:Evil 1999:Self 1949:and 1839:Blum 1550:and 1354:Lobb 1309:Cake 1304:Bell 1054:Star 961:Ulam 860:Pell 649:Cube 110:OEIS 2437:Ban 1825:or 1344:Lah 112:). 16:An 2567:: 136:, 2553:e 2546:t 2539:v 2528:. 709:a 590:e 583:t 576:v 225:e 218:t 211:v 98:. 84:2 80:) 77:2 74:+ 71:n 68:5 60:2 56:n 52:5 49:( 46:n 30:n

Index

figurate number
icosahedron
A006564
OEIS
René Descartes
Johann Faulhaber
polygonal numbers
pyramidal numbers
cubes
Platonic solids
semiregular polyhedra
Friedrich Wilhelm Marpurg
Georg Simon KlĂĽgel
Sir Frederick Pollock
Federico, Pasquale Joseph
Descartes on Polyhedra: A Study of the "De solidorum elementis"
v
t
e
Figurate numbers
2-dimensional
centered
Centered triangular numbers
Centered square numbers
Centered pentagonal numbers
Centered hexagonal numbers
Centered heptagonal numbers
Centered octagonal numbers
Centered nonagonal numbers
Centered decagonal numbers

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