1252:
923:
1245:
1323:
1376:
1238:
1356:
958:
944:
951:
930:
740:
1128:
937:
731:
1339:
493:
542:
226:
1177:
1156:
1170:
1163:
1142:
968:
892:
899:
1135:
252:
878:
871:
692:
26:
885:
1259:
1149:
906:
426:
molecule has a structure based on the square antiprism, in which the eight atoms occupy the eight vertices of the antiprism, and the eight triangle-triangle edges of the antiprism correspond to single
363:, which is based on the general principle of maximizing the distances between points, a square antiprism is the favoured geometry when eight pairs of electrons surround a central
713:
703:
337:
of distances between points), maximising the distance of each point to the nearest point, or minimising the sum of all reciprocals of squares of distances between points.
151:
141:
131:
113:
103:
723:
123:
708:
136:
108:
718:
146:
118:
391:; however, the molecule is distorted away from the idealized square antiprism. Very few ions are cubical because such a shape would cause large repulsion between
1635:
1441:
Peterson, W.; Holloway, H.; Coyle, A.; Williams, M. (Sep 1971). "Antiprismatic
Coordination about Xenon: the Structure of Nitrosonium Octafluoroxenate(VI)".
1600:
479:
excavated around the sides. However, after this it can no longer be triangulated into tetrahedra without adding new vertices. It has half of the
450:) has the shape of an extremely tall tapering square antiprism. It is not a true antiprism because of its taper: the top square has half the
807:
325:
with the aim of maximising the distance between them in some sense, the resulting shape corresponds to a square antiprism rather than a
480:
1628:
1375:
175:
1329:
346:
241:
1585:
1322:
651:) are other Johnson solids that, like the square antiprism, consist of two squares and an even number of equilateral triangles.
618:) is another deltahedron, constructed by replacing the two squares of a square antiprism by pairs of equilateral triangles. The
1516:
1054:
164:
1355:
1621:
1294:
443:
1536:
1428:
1077:
159:
388:
800:
1082:
578:
1338:
2037:
559:
36:
629:) can be seen as a square antiprism with a chain of equilateral triangles inserted around the middle. The
1834:
1775:
1284:
1224:
1214:
1204:
1864:
1824:
1219:
1209:
793:
245:
1251:
1859:
1854:
1047:
1279:
334:
207:
1965:
1960:
1839:
1745:
1289:
922:
1829:
1770:
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1705:
1549:
1345:
681:
439:
292:
2042:
1849:
1765:
1720:
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1385:
1365:
859:
674:
619:
1809:
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1040:
975:
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841:
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601:
529:
230:
43:
1607:
8:
1975:
1844:
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1688:
846:
772:
768:
1454:
1244:
1990:
1955:
1814:
1709:
1658:
1482:
1274:
1199:
780:
525:
521:
472:
447:
356:
296:
192:
1591:
73:
1970:
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1755:
1699:
1568:
1532:
1512:
1474:
1466:
1424:
1237:
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604:) constructed by replacing both squares of a square antiprism with a square pyramid.
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1909:
1500:
1458:
641:
310:
1462:
1012:
957:
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326:
288:
202:
95:
950:
739:
1730:
1653:
1571:
929:
659:
574:
427:
85:
2031:
1935:
1791:
1725:
1470:
1127:
1016:
936:
730:
563:
468:
1478:
630:
541:
492:
352:
225:
1176:
759:, the square antiprism belongs to a family of polyhedra that includes the
1169:
1162:
1155:
1141:
589:
476:
273:
329:. Specific methods of distributing the points include, for example, the
2000:
1888:
1678:
1645:
891:
829:
822:
760:
593:
217:
1134:
898:
1995:
1985:
1930:
1914:
1750:
1576:
1194:
967:
877:
787:
756:
419:
360:
269:
870:
1881:
1613:
1400:
884:
691:
513:
368:
261:
251:
25:
2005:
1980:
1531:
The facts on file: Geometry handbook, Catherine A. Gorini, 2003,
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can be made (clockwise or counterclockwise) with the same
372:
763:(which can be seen as a triangle-capped antiprism), the
321:
When eight points are distributed on the surface of a
532:
is 3.3/2.3.4, with one triangle retrograde. It has d
457:
1594:www.georgehart.com: The Encyclopedia of Polyhedra
1566:
1499:
2029:
371:with this geometry is the octafluoroxenate(VI)
524:, but it can't be made uniform; the sides are
1629:
1048:
801:
341:Molecules with square antiprismatic geometry
475:. It can be seen as the convex form with 4
1636:
1622:
1055:
1041:
808:
794:
658:can be truncated and alternated to form a
276:sequence of triangle sides closed by two
256:3D model of a (uniform) square antiprism
249:
1434:
1330:Square antiprismatic molecular geometry
347:Square antiprismatic molecular geometry
268:is the second in an infinite family of
242:Square antiprismatic molecular geometry
2030:
1423:, Academic Press, Italy, p. 299.
1033:2 symmetry mutations of snub tilings:
309:-symmetric variant is the cell of the
1617:
1567:
316:
1643:
750:
553:
548:
499:
13:
573:) constructed by augmenting one a
433:
14:
2054:
1560:
458:Topologically identical polyhedra
1374:
1354:
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1243:
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1175:
1168:
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956:
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897:
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883:
876:
869:
738:
729:
721:
716:
711:
706:
701:
690:
540:
491:
462:
389:nitrosonium octafluoroxenate(VI)
224:
149:
144:
139:
134:
129:
121:
116:
111:
106:
101:
24:
438:The main building block of the
333:(minimizing the sum of all the
250:
1542:
1525:
1493:
1413:
579:gyroelongated square bipyramid
313:square antiprismatic 72-cell.
1:
1463:10.1126/science.173.4003.1238
418:molecules as its most stable
280:caps. It is also known as an
2016:Degenerate polyhedra are in
1550:"Pictures of Twisted Prisms"
688:
560:gyroelongated square pyramid
407:is one of the few examples.
37:Prismatic uniform polyhedron
15:
7:
1835:pentagonal icositetrahedron
1776:truncated icosidodecahedron
1394:
1314:
10:
2059:
1865:pentagonal hexecontahedron
1825:deltoidal icositetrahedron
483:of the uniform solution: D
344:
246:Square antiprismatic prism
239:
2014:
1948:
1923:
1905:
1898:
1873:
1860:disdyakis triacontahedron
1855:deltoidal hexecontahedron
1789:
1697:
1652:
1592:Virtual Reality Polyhedra
1505:Chemistry of the Elements
1503:; Earnshaw, Alan (1997).
1086:
1076:
1065:
1028:
410:In addition, the element
223:
32:
23:
19:Uniform square antiprism
18:
1406:
1011:is first in a series of
506:crossed square antiprism
442:(at the site of the old
240:Not to be confused with
208:Tetragonal trapezohedron
1966:gyroelongated bipyramid
1840:rhombic triacontahedron
1746:truncated cuboctahedron
918:Spherical tiling image
1961:truncated trapezohedra
1830:disdyakis dodecahedron
1796:(duals of Archimedean)
1771:rhombicosidodecahedron
1761:truncated dodecahedron
1346:One World Trade Center
440:One World Trade Center
430:between sulfur atoms.
293:semiregular polyhedron
257:
1850:pentakis dodecahedron
1766:truncated icosahedron
1721:truncated tetrahedron
1509:Butterworth-Heinemann
1501:Greenwood, Norman N.
1382:Snub square antiprism
860:Apeirogonal antiprism
620:snub square antiprism
602:equilateral triangles
287:If all its faces are
255:
2038:Prismatoid polyhedra
1810:rhombic dodecahedron
1736:truncated octahedron
852:Heptagonal antiprism
842:Pentagonal antiprism
830:Triangular antiprism
765:pentagonal antiprism
530:vertex configuration
170:, , (2*4), order 16
1845:triakis icosahedron
1820:tetrakis hexahedron
1805:triakis tetrahedron
1741:rhombicuboctahedron
1455:1971Sci...173.1238P
1449:(4003): 1238–1239.
1421:Inorganic Chemistry
1087:Compact hyperbolic
963:Plane tiling image
847:Hexagonal antiprism
815:
773:octagonal antiprism
769:hexagonal antiprism
667:
536:symmetry, order 8.
526:isosceles triangles
454:of the bottom one.
184:, , (442), order 8
1815:triakis octahedron
1700:Archimedean solids
1569:Weisstein, Eric W.
1386:Matemateca IME-USP
1366:Matemateca Ime-USP
778:
665:
522:vertex arrangement
473:vertex arrangement
448:September 11, 2001
444:World Trade Center
357:molecular geometry
317:Points on a sphere
297:uniform polyhedron
258:
2025:
2024:
1944:
1943:
1781:snub dodecahedron
1756:icosidodecahedron
1588:interactive model
1518:978-0-08-037941-8
1419:Holleman-Wiberg.
1312:
1311:
1308:V3.3.4.3.∞
1015:and tilings with
1005:
1004:
866:Polyhedron image
823:Digonal antiprism
751:Symmetry mutation
748:
747:
577:. Similarly, the
554:Derived polyhedra
549:Related polyhedra
516:identical to the
500:Crossed antiprism
414:forms octatomic S
351:According to the
238:
237:
2050:
1903:
1902:
1899:Dihedral uniform
1874:Dihedral regular
1797:
1713:
1662:
1638:
1631:
1624:
1615:
1614:
1586:Square Antiprism
1582:
1581:
1554:
1553:
1546:
1540:
1529:
1523:
1522:
1511:. p. 1275.
1507:(2nd ed.).
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1417:
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1362:Square antiprism
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1247:
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1165:
1158:
1151:
1144:
1137:
1130:
1057:
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1026:
1025:
1009:square antiprism
970:
960:
953:
946:
939:
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837:Square antiprism
816:
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714:
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666:Snub antiprisms
664:
656:square antiprism
642:sphenomegacorona
544:
518:square antiprism
495:
406:
405:
404:
386:
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384:
266:square antiprism
254:
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1949:Dihedral others
1940:
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1894:
1869:
1798:
1795:
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1703:
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1693:
1656:
1654:Platonic solids
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1317:
1232:
1225:3.3.4.3.∞
1122:
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1061:
835:
828:
819:Antiprism name
814:
753:
743:
734:
722:
717:
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707:
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700:
699:
695:
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628:
617:
609:snub disphenoid
587:
572:
566:(specifically,
556:
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510:star polyhedron
502:
486:
465:
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436:
434:In architecture
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331:Thomson problem
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100:
96:Coxeter diagram
79:
74:Schläfli symbol
56:
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11:
5:
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1792:Catalan solids
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1783:
1778:
1773:
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1731:truncated cube
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1608:polyhedronisme
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1561:External links
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1013:snub polyhedra
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976:Vertex config.
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660:snub antiprism
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575:square pyramid
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520:with the same
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428:covalent bonds
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387:) in the salt
381:
345:Main article:
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176:Rotation group
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160:Symmetry group
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86:Wythoff symbol
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65:Faces by sides
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1537:0-8160-4875-4
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584:
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564:Johnson solid
561:
543:
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531:
527:
523:
519:
515:
514:topologically
511:
507:
494:
490:
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482:
478:
474:
470:
469:twisted prism
463:Twisted prism
455:
453:
449:
446:destroyed on
445:
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328:
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314:
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305:
302:A nonuniform
300:
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285:
283:
279:
275:
274:even-numbered
272:formed by an
271:
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231:Vertex figure
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99:
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90:| 2 2 4
89:
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50:
47:
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42:
41:
38:
35:
31:
27:
22:
17:
2043:Snub tilings
2017:
1936:trapezohedra
1887:
1880:
1684:dodecahedron
1575:
1544:
1527:
1504:
1495:
1446:
1442:
1436:
1420:
1415:
1189:
1070:
1034:
1030:
1020:
1008:
1006:
836:
834:(Tetragonal)
783:
754:
655:
653:
645:
634:
631:sphenocorona
623:
612:
606:
582:
567:
557:
517:
505:
503:
477:tetrahedrons
466:
437:
409:
353:VSEPR theory
350:
320:
303:
301:
286:
281:
265:
259:
60:= 8 (χ = 2)
57:
52:
48:
1706:semiregular
1689:icosahedron
1669:tetrahedron
1572:"Antiprism"
1305:V3.3.4.3.8
1302:V3.3.4.3.7
1299:V3.3.4.3.6
590:deltahedron
335:reciprocals
2032:Categories
2001:prismatoid
1931:bipyramids
1915:antiprisms
1889:hosohedron
1679:octahedron
1295:V3.3.4.3.5
1290:V3.3.4.3.4
1285:V3.3.4.3.3
1280:V3.3.4.3.2
1116:∞42
1090:Paracomp.
827:(Trigonal)
788:antiprisms
779:Family of
771:, and the
761:octahedron
682:Alternated
671:Antiprism
640:) and the
594:polyhedron
291:, it is a
270:antiprisms
214:Properties
189:References
68:8{3}+2{4}
1996:birotunda
1986:bifrustum
1751:snub cube
1646:polyhedra
1577:MathWorld
1471:0036-8075
1220:3.3.4.3.8
1215:3.3.4.3.7
1210:3.3.4.3.6
1205:3.3.4.3.5
1200:3.3.4.3.4
1195:3.3.4.3.3
1190:3.3.4.3.2
1083:Euclidean
1078:Spherical
1035:3.3.4.3.n
757:antiprism
675:Truncated
487:order 4.
420:allotrope
361:chemistry
1976:bicupola
1956:pyramids
1882:dihedron
1487:22384146
1479:17775218
1401:Biscornu
1395:See also
1348:building
1315:Examples
1233:figures
1123:figures
1066:Symmetry
1019:3.3.4.3.
1001:∞.3.3.3
995:7.3.3.3
992:6.3.3.3
989:5.3.3.3
986:4.3.3.3
983:3.3.3.3
980:2.3.3.3
744:ss{2,8}
735:ts{2,8}
600:are all
481:symmetry
369:molecule
282:anticube
262:geometry
234:3.3.3.4
80:sr{2,4}
44:Elements
2018:italics
2006:scutoid
1991:rotunda
1981:frustum
1710:uniform
1659:regular
1644:Convex
1539:, p.172
1451:Bibcode
1443:Science
1275:Config.
1185:Config.
786:-gonal
781:uniform
588:) is a
422:. The S
393:ligands
289:regular
278:polygon
1971:cupola
1924:duals:
1910:prisms
1535:
1515:
1485:
1477:
1469:
1427:
767:, the
755:As an
697:s{2,8}
596:whose
528:. Its
412:sulfur
367:. One
323:sphere
264:, the
218:convex
78:s{2,8}
51:= 10,
1601:model
1483:S2CID
1407:Notes
598:faces
562:is a
508:is a
311:noble
196:77(b)
1674:cube
1598:VRML
1533:ISBN
1513:ISBN
1475:PMID
1467:ISSN
1425:ISBN
1384:(at
1364:(at
1231:Gyro
1121:Snub
1113:842
1110:742
1107:642
1104:542
1101:442
1098:342
1095:242
1007:The
998:...
911:...
856:...
654:The
607:The
558:The
452:area
365:atom
327:cube
244:and
203:Dual
55:= 16
33:Type
1708:or
1459:doi
1447:173
685:ht
592:(a
397:PaF
377:XeF
373:ion
359:in
355:of
295:or
260:In
2034::
1610:A4
1574:.
1481:.
1473:.
1465:.
1457:.
1445:.
1023:.
775:.
678:t
662::
649:88
638:86
627:85
616:84
586:17
571:10
534:4d
512:,
504:A
467:A
395:;
299:.
284:.
167:4d
2020:.
1712:)
1704:(
1661:)
1657:(
1637:e
1630:t
1623:v
1580:.
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1489:.
1461::
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1431:.
1388:)
1368:)
1073:2
1071:n
1069:4
1056:e
1049:t
1042:v
1031:n
1029:4
1021:n
809:e
802:t
795:v
784:n
646:J
644:(
635:J
633:(
624:J
622:(
613:J
611:(
583:J
581:(
568:J
485:4
424:8
416:8
402:8
382:8
375:(
307:4
304:D
193:U
182:4
180:D
165:D
58:V
53:E
49:F
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