345:
354:
177:
406:
186:
394:
166:
157:
95:
560:
266:: the pyramids are symmetrical as they rotated around their axis of symmetry (a line passing through the apex and the base centroid), and they are mirror symmetric relative to any perpendicular plane passing through a bisector of the base. Examples are
86:, the term evolved to "πυραμίδα" (pyramída), continuing to denote pyramid structures. The Greek term "πυραμίς" was borrowed into Latin as "pyramis." The term "πυραμίδα" influenced the evolution of the word into "pyramid" in English and other languages.
204:
is a pyramid where the base is circumscribed about the circle and the altitude of the pyramid meets at the circle's center. This pyramid may be classified based on the regularity of its bases. A pyramid with a regular polygon as the base is called a
78:
term "πυραμίς" (pyramis), which referred to a pyramid-shaped structure and a type of wheat cake. The term is rooted in the Greek "πυρ" (pyr, 'fire') and "άμις" (amis, 'vessel'), highlighting the shape's pointed, flame-like appearance.
608:
dimensional hyperplane. A point called the apex is located outside the hyperplane and gets connected to all the vertices of the polytope and the distance of the apex from the hyperplane is called height.
679:
1589:
529:
446:
The surface area is the total area of each polyhedra's faces. In the case of a pyramid, its surface area is the sum of the area of triangles and the area of the polygonal base.
422:
The type of pyramids can be derived in many ways. The base regularity of a pyramid's base may be classified based on the type of polygon, and one example is the pyramid with
58:
with a polygonal base. Many types of pyramids can be found by determining the shape of bases, or cutting off the apex. It can be generalized into higher dimension, known as
300:
or triangular pyramid is an example that has four equilateral triangles, with all edges equal in length, and one of them is considered as the base. Because the faces are
487:
467:
576:
dimensional space. In the case of the pyramid, one connects all vertices of the base, a polygon in a plane, to a point outside the plane, which is the
1582:
535:, suggesting they acquainted the volume of a square pyramid. The formula of volume for a general pyramid was discovered by Indian mathematician
1517:
1487:
1425:
1394:
1367:
1333:
1298:
1228:
1201:
1108:
1081:
1053:
1026:
945:
1575:
1317:
ICGG 2018 - Proceedings of the 18th
International Conference on Geometry and Graphics: 40th Anniversary - Milan, Italy, August 3-7, 2018
937:
1400:
274:, a four- and five-triangular faces pyramid with a square and pentagon base, respectively; they are classified as the first and second
999:
896:
758:
633:
775:
The word meant "a kind of cake of roasted wheat-grains preserved in honey"; the
Egyptian pyramids were named after its form. See
1129:
1124:
1069:
124:
defined a pyramid as a solid figure, constructed from one plane to one point. The context of his definition was vague until
2001:
492:
2011:
1996:
194:
The family of a regular polygonal base pyramid: tetrahedron, square pyramid, pentagonal pyramid, and hexagonal pyramid.
1788:
1729:
913:
1818:
1778:
2016:
1813:
1808:
135:
is defined as a polyhedron where its vertices lie on two parallel planes, with its lateral faces are triangles,
868:
1919:
1914:
1793:
1699:
1314:
Wohlleben, Eva (2019), "Duality in Non-Polyhedral Bodies Part I: Polyliner", in
Cocchiarella, Luigi (ed.),
1783:
1724:
1714:
1659:
580:. The pyramid's height is the distance of the peak from the plane. This construction gets generalized to
1803:
1719:
1674:
114:. Historically, the definition of a pyramid has been described by many mathematicians in ancient times.
1763:
1689:
1637:
423:
313:
120:
115:
63:
102:
A pyramid is a polyhedron that may be formed by connecting a polygonal base and a point, called the
1929:
1798:
1773:
1758:
1694:
1642:
777:
329:
125:
531:
The volume of a pyramid was recorded back in ancient Egypt, where they calculated the volume of a
1991:
1944:
1768:
1663:
1612:
1458:
1320:, Advances in Intelligent Systems and Computing, vol. 809, Springer, p. 485–486,
1269:
1261:
1156:
271:
244:
240:
328:, meaning their duals are the same as vertices corresponding to the edges and vice versa. Their
449:
The volume of a pyramid is the one-third product of the base's area and the height. Given that
368:
A right pyramid may also have a base with an irregular polygon. Examples are the pyramids with
2006:
1924:
1734:
1709:
1653:
1550:
1513:
1483:
1421:
1415:
1390:
1363:
1329:
1315:
1294:
1288:
1224:
1218:
1197:
1104:
1077:
1049:
1022:
995:
989:
941:
892:
1507:
1477:
1384:
1349:
1183:
1098:
1043:
1016:
931:
886:
1863:
1450:
1355:
1321:
1253:
1189:
1164:
1138:
970:
545:
that the volume of a pyramid is incorrectly the half product of area's base and the height.
1152:
344:
1168:
1148:
577:
321:
301:
103:
83:
47:
1441:
Gillings, R. J. (1964), "The volume of a truncated pyramid in ancient
Egyptian papyri",
559:
1684:
1607:
472:
452:
305:
267:
353:
1985:
1889:
1745:
1679:
1273:
1160:
275:
140:
75:
1509:
An
Introduction to Geometrical Probability: Distributional Aspects with Applications
278:
if their regular faces and edges that are equal in length, and their symmetries are
554:
59:
176:
17:
1622:
1087:. See Chapter 11: Finite Symmetry Groups, 11.3 Pyramids, Prisms, and Antiprisms.
541:
405:
333:
297:
185:
110:. The edges connected from the polygonal base's vertices to the apex are called
434:; if the truncation plane is parallel to the base of a pyramid, it is called a
1954:
1842:
1632:
1599:
1359:
1325:
1193:
1185:
Introduction to
Computational Origami: The World of New Computational Geometry
309:
132:
128:
defined it as the figure by putting the point together with a polygonal base.
39:
1553:
1949:
1939:
1884:
1868:
1704:
1558:
1536:
1045:
The
Experimenter's A-Z of Mathematics: Math Activities with Computer Support
536:
412:
369:
325:
165:
136:
1143:
393:
1835:
1454:
991:
Mathematics and
Plausible Reasoning: Induction and analogy in mathematics
31:
1462:
489:
is the height of a pyramid. Mathematically, the volume of a pyramid is:
156:
1959:
1934:
1265:
974:
532:
435:
373:
43:
759:"Henry George Liddell, Robert Scott, A Greek-English Lexicon, πυραμίς"
317:
1257:
1567:
94:
558:
93:
1627:
933:
A Mathematical Space
Odyssey: Solid Geometry in the 21st Century
55:
1571:
106:. Each base edge and apex form an isosceles triangle, called a
1220:
The
Routledge International Handbook of Innovation Education
1482:(5th ed.), American Mathematical Society, p. 87,
724:
the height, that is the distance between the apex and the
376:
as their bases. These two pyramids have the symmetry of
567:
The hyperpyramid is the generalization of a pyramid in
918:, vol. 3, Cambridge University Press, p. 268
811:
636:
630:
dimensional hyperpyramid can be computed as follows:
495:
475:
455:
1414:
Alexander, Daniel C.; Koeberlin, Geralyn M. (2014),
50:. Each base edge and apex form a triangle, called a
1902:
1877:
1852:
1827:
1743:
1651:
1606:
673:
523:
481:
461:
961:Grünbaum, Branko (1997), "Isogonal Prismatoids",
1420:(6th ed.), Cengage Learning, p. 403,
1127:(1966), "Convex polyhedra with regular faces",
563:4-dimensional hyperpyramid with a cube as base
1583:
1512:, Taylor & Francis, p. 42–43,
1348:Pisanski, Tomaž; Servatius, Brigitte (2013),
796:Liddell, Henry George; Scott, Robert (1940).
430:. The pyramid cut off by a plane is called a
8:
854:Harper's Dictionary of Classical Antiquities
674:{\displaystyle V_{n}={\frac {A\cdot h}{n}}.}
994:, Princeton University Press, p. 138,
837:Lewis, Charlton T.; Short, Charles (1879).
735:dimensional hyperplane containing the base
362:Pyramids with rectangular and rhombic bases
1856:
1590:
1576:
1568:
1389:, Cambridge University Press, p. 50,
915:Euclid: The Thirteen Books of the Elements
1501:
1499:
1142:
930:Alsina, Claudi; Nelsen, Roger B. (2015),
650:
641:
635:
502:
494:
474:
454:
143:. Pyramids are classified as prismatoid.
1417:Elementary Geometry for College Students
1351:Configuration from a Graphical Viewpoint
873:, Cambridge University Press, p. 13
701:dimensional volume of the hyperpyramid.
399:A pyramid truncated by an inclined plane
1290:The Humongous Book of Geometry Problems
1244:Cundy, H. Martyn (1952), "Deltahedra",
1100:An Introduction to the Theory of Groups
750:
1021:, John Wiley & Sons, p. 10,
963:Discrete & Computational Geometry
891:, John Wiley & Sons, p. 98,
7:
1048:, Taylor & Francis, p. 23,
74:The word "pyramid" derives from the
938:Mathematical Association of America
718:dimensional volume of the base and
524:{\displaystyle V={\frac {1}{3}}Bh.}
1103:, Dover Publications, p. 48,
25:
27:Conic solid with a polygonal base
782:Etymological Dictionary of Greek
404:
392:
352:
343:
324:. Pyramids have the property of
184:
175:
164:
155:
1403:from the original on 2013-12-11
1130:Canadian Journal of Mathematics
586:dimensions. The base becomes a
1293:, Penguin Group, p. 455,
1076:, Cambridge University Press,
1074:Geometries and Transformations
1:
1383:Wenninger, Magnus J. (1974),
1217:Shavinina, Larisa V. (2013),
852:Peck, Harry Thurston (1898).
316:. A pyramid with the base as
296:of order 10, respectively. A
46:base and a point, called the
1970:Degenerate polyhedra are in
1789:pentagonal icositetrahedron
1730:truncated icosidodecahedron
1287:Kelley, W. Michael (2009),
867:Cromwell, Peter R. (1997),
218:sided regular base, it has
2033:
1819:pentagonal hexecontahedron
1779:deltoidal icositetrahedron
1223:, Routledge, p. 333,
1097:Alexandroff, Paul (2012),
552:
426:as its base, known as the
332:may be represented as the
209:. For the pyramid with an
1968:
1859:
1814:disdyakis triacontahedron
1809:deltoidal hexecontahedron
1360:10.1007/978-0-8176-8364-1
1326:10.1007/978-3-319-95588-9
1194:10.1007/978-981-15-4470-5
1015:O'Leary, Michael (2010),
539:, where he quoted in his
1476:Cajori, Florian (1991),
1354:, Springer, p. 21,
1246:The Mathematical Gazette
1188:, Springer, p. 62,
1172:. See table III, line 1.
885:Smith, James T. (2000),
856:. Harper & Brothers.
621:dimensional volume of a
304:, it is an example of a
239:edges. Such pyramid has
147:Classification and types
1920:gyroelongated bipyramid
1794:rhombic triacontahedron
1700:truncated cuboctahedron
1443:The Mathematics Teacher
1182:Uehara, Ryuhei (2020),
1018:Revolutions of Geometry
798:A Greek–English Lexicon
469:is the base's area and
42:formed by connecting a
1915:truncated trapezohedra
1784:disdyakis dodecahedron
1750:(duals of Archimedean)
1725:rhombicosidodecahedron
1715:truncated dodecahedron
1506:Mathai, A. M. (1999),
1479:History of Mathematics
1144:10.4153/cjm-1966-021-8
1042:Humble, Steve (2016),
912:Heath, Thomas (1908),
675:
564:
525:
483:
463:
259:, a symmetry of order
99:
1804:pentakis dodecahedron
1720:truncated icosahedron
1675:truncated tetrahedron
784:, Brill, p. 1261
763:www.perseus.tufts.edu
676:
562:
526:
484:
464:
97:
2002:Prismatoid polyhedra
1764:rhombic dodecahedron
1690:truncated octahedron
1455:10.5951/MT.57.8.0552
634:
493:
473:
453:
424:regular star polygon
314:tetrahedral symmetry
2012:Pyramids (geometry)
1997:Self-dual polyhedra
1799:triakis icosahedron
1774:tetrakis hexahedron
1759:triakis tetrahedron
1695:rhombicuboctahedron
888:Methods of Geometry
243:as its faces, with
241:isosceles triangles
126:Heron of Alexandria
62:. All pyramids are
1769:triakis octahedron
1654:Archimedean solids
1551:Weisstein, Eric W.
1125:Johnson, Norman W.
1070:Johnson, Norman W.
988:Polya, G. (1954),
975:10.1007/PL00009307
841:. Clarendon Press.
839:A Latin Dictionary
800:. Clarendon Press.
671:
565:
521:
479:
459:
272:pentagonal pyramid
100:
98:Parts of a pyramid
18:Snub cubic pyramid
1979:
1978:
1898:
1897:
1735:snub dodecahedron
1710:icosidodecahedron
1519:978-90-5699-681-9
1489:978-1-4704-7059-3
1427:978-1-285-19569-8
1396:978-0-521-09859-5
1386:Polyhedron Models
1369:978-0-8176-8363-4
1335:978-3-319-95588-9
1300:978-1-61564-698-2
1230:978-0-203-38714-6
1203:978-981-15-4470-5
1110:978-0-486-48813-4
1083:978-1-107-10340-5
1055:978-1-134-13953-8
1028:978-0-470-59179-6
947:978-0-88385-358-0
778:Beekes, Robert S.
666:
510:
482:{\displaystyle h}
462:{\displaystyle B}
432:truncated pyramid
16:(Redirected from
2024:
2017:Geometric shapes
1857:
1853:Dihedral uniform
1828:Dihedral regular
1751:
1667:
1616:
1592:
1585:
1578:
1569:
1564:
1563:
1524:
1522:
1503:
1494:
1492:
1473:
1467:
1465:
1438:
1432:
1430:
1411:
1405:
1404:
1380:
1374:
1372:
1345:
1339:
1338:
1311:
1305:
1303:
1284:
1278:
1276:
1252:(318): 263–266,
1241:
1235:
1233:
1214:
1208:
1206:
1179:
1173:
1171:
1146:
1121:
1115:
1113:
1094:
1088:
1086:
1066:
1060:
1058:
1039:
1033:
1031:
1012:
1006:
1004:
985:
979:
977:
958:
952:
950:
927:
921:
919:
909:
903:
901:
882:
876:
874:
864:
858:
857:
849:
843:
842:
834:
828:
827:
825:
823:
808:
802:
801:
793:
787:
785:
773:
767:
765:
755:
740:
734:
732:
723:
717:
715:
706:
700:
698:
691:
680:
678:
677:
672:
667:
662:
651:
646:
645:
629:
627:
620:
618:
607:
605:
596:
594:
585:
575:
573:
530:
528:
527:
522:
511:
503:
488:
486:
485:
480:
468:
466:
465:
460:
408:
396:
384:
356:
347:
295:
286:
265:
258:
238:
231:
224:
217:
215:
188:
179:
168:
159:
21:
2032:
2031:
2027:
2026:
2025:
2023:
2022:
2021:
1982:
1981:
1980:
1975:
1964:
1903:Dihedral others
1894:
1873:
1848:
1823:
1752:
1749:
1748:
1739:
1668:
1657:
1656:
1647:
1610:
1608:Platonic solids
1602:
1596:
1549:
1548:
1545:
1533:
1528:
1527:
1520:
1505:
1504:
1497:
1490:
1475:
1474:
1470:
1440:
1439:
1435:
1428:
1413:
1412:
1408:
1397:
1382:
1381:
1377:
1370:
1347:
1346:
1342:
1336:
1313:
1312:
1308:
1301:
1286:
1285:
1281:
1258:10.2307/3608204
1243:
1242:
1238:
1231:
1216:
1215:
1211:
1204:
1181:
1180:
1176:
1123:
1122:
1118:
1111:
1096:
1095:
1091:
1084:
1068:
1067:
1063:
1056:
1041:
1040:
1036:
1029:
1014:
1013:
1009:
1002:
987:
986:
982:
960:
959:
955:
948:
929:
928:
924:
911:
910:
906:
899:
884:
883:
879:
866:
865:
861:
851:
850:
846:
836:
835:
831:
821:
819:
810:
809:
805:
795:
794:
790:
776:
774:
770:
757:
756:
752:
747:
736:
731: − 1)
726:
725:
719:
714: − 1)
709:
708:
702:
694:
693:
690:
682:
652:
637:
632:
631:
623:
622:
614:
613:
599:
598:
588:
587:
581:
569:
568:
557:
551:
491:
490:
471:
470:
451:
450:
444:
420:
419:
418:
417:
416:
409:
401:
400:
397:
383:
377:
366:
365:
364:
363:
359:
358:
357:
349:
348:
294:
288:
287:of order 8 and
285:
279:
260:
257:
248:
233:
226:
219:
211:
210:
207:regular pyramid
198:
197:
196:
195:
191:
190:
189:
181:
180:
171:
170:
169:
161:
160:
149:
92:
84:Byzantine Greek
72:
28:
23:
22:
15:
12:
11:
5:
2030:
2028:
2020:
2019:
2014:
2009:
2004:
1999:
1994:
1984:
1983:
1977:
1976:
1969:
1966:
1965:
1963:
1962:
1957:
1952:
1947:
1942:
1937:
1932:
1927:
1922:
1917:
1912:
1906:
1904:
1900:
1899:
1896:
1895:
1893:
1892:
1887:
1881:
1879:
1875:
1874:
1872:
1871:
1866:
1860:
1854:
1850:
1849:
1847:
1846:
1839:
1831:
1829:
1825:
1824:
1822:
1821:
1816:
1811:
1806:
1801:
1796:
1791:
1786:
1781:
1776:
1771:
1766:
1761:
1755:
1753:
1746:Catalan solids
1744:
1741:
1740:
1738:
1737:
1732:
1727:
1722:
1717:
1712:
1707:
1702:
1697:
1692:
1687:
1685:truncated cube
1682:
1677:
1671:
1669:
1652:
1649:
1648:
1646:
1645:
1640:
1635:
1630:
1625:
1619:
1617:
1604:
1603:
1597:
1595:
1594:
1587:
1580:
1572:
1566:
1565:
1544:
1543:External links
1541:
1540:
1539:
1532:
1529:
1526:
1525:
1518:
1495:
1488:
1468:
1449:(8): 552–555,
1433:
1426:
1406:
1395:
1375:
1368:
1340:
1334:
1306:
1299:
1279:
1236:
1229:
1209:
1202:
1174:
1116:
1109:
1089:
1082:
1061:
1054:
1034:
1027:
1007:
1000:
980:
953:
946:
940:, p. 85,
922:
904:
897:
877:
859:
844:
829:
818:. 12 July 2022
803:
788:
768:
749:
748:
746:
743:
686:
670:
665:
661:
658:
655:
649:
644:
640:
597:polytope in a
553:Main article:
550:
549:Generalization
547:
533:square frustum
520:
517:
514:
509:
506:
501:
498:
478:
458:
443:
440:
415:-base pyramid.
410:
403:
402:
398:
391:
390:
389:
388:
387:
381:
361:
360:
351:
350:
342:
341:
340:
339:
338:
306:Platonic solid
292:
283:
268:square pyramid
252:
193:
192:
183:
182:
174:
173:
172:
163:
162:
154:
153:
152:
151:
150:
148:
145:
141:parallelograms
91:
88:
71:
68:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2029:
2018:
2015:
2013:
2010:
2008:
2005:
2003:
2000:
1998:
1995:
1993:
1990:
1989:
1987:
1973:
1967:
1961:
1958:
1956:
1953:
1951:
1948:
1946:
1943:
1941:
1938:
1936:
1933:
1931:
1928:
1926:
1923:
1921:
1918:
1916:
1913:
1911:
1908:
1907:
1905:
1901:
1891:
1888:
1886:
1883:
1882:
1880:
1876:
1870:
1867:
1865:
1862:
1861:
1858:
1855:
1851:
1845:
1844:
1840:
1838:
1837:
1833:
1832:
1830:
1826:
1820:
1817:
1815:
1812:
1810:
1807:
1805:
1802:
1800:
1797:
1795:
1792:
1790:
1787:
1785:
1782:
1780:
1777:
1775:
1772:
1770:
1767:
1765:
1762:
1760:
1757:
1756:
1754:
1747:
1742:
1736:
1733:
1731:
1728:
1726:
1723:
1721:
1718:
1716:
1713:
1711:
1708:
1706:
1703:
1701:
1698:
1696:
1693:
1691:
1688:
1686:
1683:
1681:
1680:cuboctahedron
1678:
1676:
1673:
1672:
1670:
1665:
1661:
1655:
1650:
1644:
1641:
1639:
1636:
1634:
1631:
1629:
1626:
1624:
1621:
1620:
1618:
1614:
1609:
1605:
1601:
1593:
1588:
1586:
1581:
1579:
1574:
1573:
1570:
1561:
1560:
1555:
1552:
1547:
1546:
1542:
1538:
1535:
1534:
1530:
1521:
1515:
1511:
1510:
1502:
1500:
1496:
1491:
1485:
1481:
1480:
1472:
1469:
1464:
1460:
1456:
1452:
1448:
1444:
1437:
1434:
1429:
1423:
1419:
1418:
1410:
1407:
1402:
1398:
1392:
1388:
1387:
1379:
1376:
1371:
1365:
1361:
1357:
1353:
1352:
1344:
1341:
1337:
1331:
1327:
1323:
1319:
1318:
1310:
1307:
1302:
1296:
1292:
1291:
1283:
1280:
1275:
1271:
1267:
1263:
1259:
1255:
1251:
1247:
1240:
1237:
1232:
1226:
1222:
1221:
1213:
1210:
1205:
1199:
1195:
1191:
1187:
1186:
1178:
1175:
1170:
1166:
1162:
1158:
1154:
1150:
1145:
1140:
1136:
1132:
1131:
1126:
1120:
1117:
1112:
1106:
1102:
1101:
1093:
1090:
1085:
1079:
1075:
1071:
1065:
1062:
1057:
1051:
1047:
1046:
1038:
1035:
1030:
1024:
1020:
1019:
1011:
1008:
1003:
1001:0-691-02509-6
997:
993:
992:
984:
981:
976:
972:
968:
964:
957:
954:
949:
943:
939:
935:
934:
926:
923:
917:
916:
908:
905:
900:
898:0-471-25183-6
894:
890:
889:
881:
878:
872:
871:
863:
860:
855:
848:
845:
840:
833:
830:
817:
813:
807:
804:
799:
792:
789:
783:
779:
772:
769:
764:
760:
754:
751:
744:
742:
739:
730:
722:
713:
705:
697:
689:
685:
668:
663:
659:
656:
653:
647:
642:
638:
626:
617:
610:
603:
592:
584:
579:
572:
561:
556:
548:
546:
544:
543:
538:
534:
518:
515:
512:
507:
504:
499:
496:
476:
456:
447:
441:
439:
437:
433:
429:
425:
414:
407:
395:
386:
380:
375:
371:
355:
346:
337:
335:
331:
327:
323:
319:
315:
312:, and it has
311:
307:
303:
299:
291:
282:
277:
276:Johnson solid
273:
269:
264:
255:
251:
246:
242:
237:
229:
222:
214:
208:
203:
202:right pyramid
187:
178:
167:
158:
146:
144:
142:
138:
134:
129:
127:
123:
122:
117:
113:
112:lateral edges
109:
105:
96:
89:
87:
85:
80:
77:
76:ancient Greek
69:
67:
65:
61:
57:
53:
49:
45:
41:
37:
33:
19:
1971:
1909:
1890:trapezohedra
1841:
1834:
1638:dodecahedron
1557:
1508:
1478:
1471:
1446:
1442:
1436:
1416:
1409:
1385:
1378:
1350:
1343:
1316:
1309:
1289:
1282:
1249:
1245:
1239:
1219:
1212:
1184:
1177:
1134:
1128:
1119:
1099:
1092:
1073:
1064:
1044:
1037:
1017:
1010:
990:
983:
966:
962:
956:
932:
925:
914:
907:
887:
880:
869:
862:
853:
847:
838:
832:
820:. Retrieved
815:
806:
797:
791:
781:
771:
762:
753:
737:
728:
720:
711:
707:denotes the
703:
695:
692:denotes the
687:
683:
624:
615:
611:
601:
590:
582:
570:
566:
555:Hyperpyramid
540:
448:
445:
431:
428:star pyramid
427:
421:
385:of order 4.
378:
367:
320:is known as
289:
280:
262:
253:
249:
245:its symmetry
235:
227:
220:
212:
206:
201:
199:
130:
119:
111:
108:lateral face
107:
101:
81:
73:
60:hyperpyramid
52:lateral face
51:
35:
29:
1660:semiregular
1643:icosahedron
1623:tetrahedron
1137:: 169–200,
542:Aryabhatiya
442:Mensuration
334:wheel graph
298:tetrahedron
232:faces, and
56:conic solid
1986:Categories
1955:prismatoid
1885:bipyramids
1869:antiprisms
1843:hosohedron
1633:octahedron
1169:0132.14603
816:Wiktionary
812:"πυραμίδα"
745:References
310:deltahedra
225:vertices,
137:trapezoids
133:prismatoid
90:Definition
54:. It is a
40:polyhedron
1992:Polyhedra
1950:birotunda
1940:bifrustum
1705:snub cube
1600:polyhedra
1559:MathWorld
1554:"Pyramid"
1537:Bipyramid
1274:250435684
1161:122006114
969:: 13–52,
870:Polyhedra
657:⋅
537:Aryabhata
413:pentagram
370:rectangle
326:self-dual
70:Etymology
64:self-dual
44:polygonal
2007:Pyramids
1930:bicupola
1910:pyramids
1836:dihedron
1531:See also
1463:27957144
1401:archived
1072:(2018),
780:(2009),
330:skeleton
121:Elements
116:Euclides
32:geometry
1972:italics
1960:scutoid
1945:rotunda
1935:frustum
1664:uniform
1613:regular
1598:Convex
1266:3608204
1153:0185507
822:30 June
436:frustum
374:rhombus
302:regular
118:in his
36:pyramid
1925:cupola
1878:duals:
1864:prisms
1516:
1486:
1461:
1424:
1393:
1366:
1332:
1297:
1272:
1264:
1227:
1200:
1167:
1159:
1151:
1107:
1080:
1052:
1025:
998:
944:
895:
318:circle
139:, and
1459:JSTOR
1270:S2CID
1262:JSTOR
1157:S2CID
681:Here
38:is a
1628:cube
1514:ISBN
1484:ISBN
1422:ISBN
1391:ISBN
1364:ISBN
1330:ISBN
1295:ISBN
1225:ISBN
1198:ISBN
1105:ISBN
1078:ISBN
1050:ISBN
1023:ISBN
996:ISBN
942:ISBN
893:ISBN
824:2024
612:The
604:− 1)
593:− 1)
578:peak
372:and
322:cone
308:and
270:and
104:apex
48:apex
34:, a
1662:or
1451:doi
1356:doi
1322:doi
1254:doi
1190:doi
1165:Zbl
1139:doi
971:doi
247:is
230:+ 1
223:+ 1
82:In
30:In
1988::
1556:.
1498:^
1457:,
1447:57
1445:,
1399:,
1362:,
1328:,
1268:,
1260:,
1250:36
1248:,
1196:,
1163:,
1155:,
1149:MR
1147:,
1135:18
1133:,
967:18
965:,
936:,
814:.
761:,
741:.
438:.
411:A
382:2v
336:.
293:5v
284:4v
200:A
131:A
66:.
1974:.
1666:)
1658:(
1615:)
1611:(
1591:e
1584:t
1577:v
1562:.
1523:.
1493:.
1466:.
1453::
1431:.
1373:.
1358::
1324::
1304:.
1277:.
1256::
1234:.
1207:.
1192::
1141::
1114:.
1059:.
1032:.
1005:.
978:.
973::
951:.
920:.
902:.
875:.
826:.
786:.
766:.
738:A
733:-
729:n
727:(
721:h
716:-
712:n
710:(
704:A
699:-
696:n
688:n
684:V
669:.
664:n
660:h
654:A
648:=
643:n
639:V
628:-
625:n
619:-
616:n
606:-
602:n
600:(
595:-
591:n
589:(
583:n
574:-
571:n
519:.
516:h
513:B
508:3
505:1
500:=
497:V
477:h
457:B
379:C
290:C
281:C
263:n
261:2
256:v
254:n
250:C
236:n
234:2
228:n
221:n
216:-
213:n
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
