40:
1268:
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1250:
1241:
1232:
1094:
1328:
627:
450:
403:
655:
814:
1002:
309:
622:{\displaystyle 12\cos \left({\frac {2\pi }{13}}\right)=2{\sqrt {26-2{\sqrt {13}}}}\cos \left({\frac {1}{3}}\arctan \left({\frac {{\sqrt {3}}\left({\sqrt {13}}+1\right)}{7-{\sqrt {13}}}}\right)\right)+{\sqrt {13}}-1.}
644:
1068:
885:
922:
725:
718:
929:
385:
442:
1097:
Symmetries of a regular tridecagon. Vertices are colored by their symmetry positions. Blue mirrors are drawn through vertices and edge. Gyration orders are given in the center.
643:
235:
1355:
2019:
1411:
1489:
1014:
1082:(a distance which would take light approximately 55 minutes to travel), the absolute error on the side length constructed would be
92:
1193:
102:
97:
1432:
110:
809:{\displaystyle a_{\text{target}}=r\cdot 2\cdot \sin \left({\frac {180^{\circ }}{13}}\right)=0.478631328575115\ldots \;}
1612:
1592:
826:
84:
894:
1587:
1544:
1519:
1160:
when reflection lines path through both edges and vertices. Cyclic symmetries in the middle column are labeled as
446:
angle trisection by means of the
Tomahawk (light blue). This construction is derived from the following equation:
1184:
1216:: {13/2}, {13/3}, {13/4}, {13/5}, and {13/6}. Since 13 is prime, none of the tridecagrams are compound figures.
1647:
332:
651:
Another possible animation of an approximate construction, also possible with using straightedge and compass.
997:{\displaystyle \mu _{\text{target}}=\left({\frac {360^{\circ }}{13}}\right)=27.{\overline {692307}}^{\circ }}
1572:
1378:
685:
1597:
1482:
637:
349:
891:
Constructed central angle of the tridecagon in GeoGebra (display significant 13 decimal places, rounded)
409:
1998:
1938:
1577:
1403:
328:
1882:
1652:
1582:
1524:
1988:
1963:
1933:
1928:
1887:
1602:
396:
336:
153:
1993:
1534:
1137:
1213:
211:
74:
39:
1973:
1567:
1475:
1450:
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1407:
1106:
402:
388:
115:
64:
1502:
1370:
654:
392:
1414:(Chapter 20, Generalized Schaefli symbols, Types of symmetry of a polygon pp. 275â278)
1267:
1258:
1249:
1240:
1231:
1167:
Each subgroup symmetry allows one or more degrees of freedom for irregular forms. Only the
1968:
1948:
1943:
1913:
1632:
1607:
1539:
1093:
218:
205:
161:
157:
60:
53:
1978:
1958:
1923:
1918:
1549:
1529:
1356:"Angle trisection, the heptagon, and the triskaidecagon p. 192â194 (p. 193 Fig.4)"
1306:
1277:
1148:. The dihedral symmetries are divided depending on whether they pass through vertices (
320:
222:
149:
145:
131:
127:
2013:
1953:
1804:
1697:
1617:
1559:
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1983:
1853:
1809:
1773:
1763:
1758:
1209:
1122:
1114:
633:
324:
304:{\displaystyle A={\frac {13}{4}}a^{2}\cot {\frac {\pi }{13}}\simeq 13.1858\,a^{2}.}
168:
1892:
1799:
1778:
1768:
1453:
1140:
labels these by a letter and group order. Full symmetry of the regular form is
1897:
1743:
1627:
1332:
1309:
17:
1872:
1862:
1839:
1829:
1819:
1748:
1657:
1622:
1458:
1327:
1136:
These 4 symmetries can be seen in 4 distinct symmetries on the tridecagon.
1877:
1867:
1824:
1783:
1712:
1702:
1692:
1511:
680:
180:
823:
Up to the maximum precision of 15 decimal places, the absolute error is
1834:
1814:
1727:
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1707:
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1637:
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192:
1642:
1374:
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1192:
653:
406:
A regular tridecagon (triskaidecagon) with radius of circumcircle
401:
658:
Tridecagon, approximate construction as an animation (3 min 30 s)
1471:
1063:{\displaystyle F_{\mu }=\mu -\mu _{\text{target}}=0.0^{\circ }}
642:
632:
An approximate construction of a regular tridecagon using
1006:
Absolute angular error of the constructed central angle:
1423:
Colin R. Bruce, II, George Cuhaj, and Thomas
Michael,
1171:
subgroup has no degrees of freedom but can be seen as
1017:
932:
897:
829:
728:
688:
453:
412:
352:
238:
346:
of a regular tridecagon with radius of circumcircle
1906:
1852:
1792:
1736:
1675:
1666:
1558:
1510:
1183:The regular tridecagon is used as the shape of the
167:
141:
126:
109:
83:
73:
59:
49:
32:
1062:
996:
916:
879:
808:
712:
621:
436:
379:
303:
1117:there is one subgroup with dihedral symmetry: Dih
1011:Up to 13 decimal places, the absolute error is
880:{\displaystyle F_{a}=a-a_{\text{target}}=0.0\;}
917:{\displaystyle \mu =27.6923076923077^{\circ }}
818:Absolute error of the constructed side length:
1483:
8:
1672:
1490:
1476:
1468:
1218:
865:
794:
698:
1054:
1041:
1022:
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988:
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931:
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896:
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828:
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764:
733:
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687:
606:
584:
558:
546:
543:
523:
503:
492:
467:
452:
413:
411:
353:
351:
292:
287:
271:
259:
245:
237:
1314:
1092:
217:The measure of each internal angle of a
1346:
647:An Approximate Tridecagon Construction.
29:
1354:Gleason, Andrew Mattei (March 1988).
1212:. There are 5 regular forms given by
713:{\displaystyle a=0.478631328575115\;}
342:The following is an animation from a
335:. However, it is constructible using
7:
1425:2007 Standard Catalog of World Coins
1078:At a circumscribed circle of radius
380:{\displaystyle {\overline {OA}}=12,}
221:tridecagon is approximately 152.308
1406:, (2008) The Symmetries of Things,
1164:for their central gyration orders.
437:{\displaystyle {\overline {OA}}=12}
327:, the regular tridecagon cannot be
25:
1363:The American Mathematical Monthly
1326:
1266:
1257:
1248:
1239:
1230:
1191:
225:, and the area with side length
100:
95:
90:
38:
2020:Polygons by the number of sides
1402:John H. Conway, Heidi Burgiel,
1074:Example to illustrate the error
663:Based on the unit circle r = 1
1305:The regular tridecagon is the
874:
866:
803:
795:
722:Side length of the tridecagon
707:
699:
191:or 13-gon is a thirteen-sided
1:
1427:, Krause Publications, 2006,
444:as an animation (1 min 44 s),
1316:
1275:
1225:
983:
926:Central angle of tridecagon
423:
363:
1144:and no symmetry is labeled
679:Constructed side length in
2036:
1221:
1113:, order 26. Since 13 is a
1156:for perpendiculars), and
339:, or an angle trisector.
37:
1152:for diagonal) or edges (
333:compass and straightedge
85:CoxeterâDynkin diagrams
1098:
1064:
998:
918:
881:
810:
714:
659:
648:
629:
623:
438:
381:
305:
1404:Chaim Goodman-Strauss
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882:
811:
715:
657:
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624:
439:
405:
382:
306:
27:Polygon with 13 edges
1723:Nonagon/Enneagon (9)
1653:Tangential trapezoid
1084:less than 1 mm.
1015:
930:
895:
827:
726:
686:
451:
410:
350:
236:
44:A regular tridecagon
1835:Megagon (1,000,000)
1603:Isosceles trapezoid
1185:Czech 20 korun coin
344:neusis construction
1805:Icositetragon (24)
1451:Weisstein, Eric W.
1103:regular tridecagon
1099:
1060:
994:
914:
877:
806:
710:
660:
649:
630:
619:
434:
377:
301:
210:is represented by
199:Regular tridecagon
33:Regular tridecagon
2007:
2006:
1848:
1847:
1825:Myriagon (10,000)
1810:Triacontagon (30)
1774:Heptadecagon (17)
1764:Pentadecagon (15)
1759:Tetradecagon (14)
1698:Quadrilateral (4)
1568:Antiparallelogram
1412:978-1-56881-220-5
1338:
1337:
1298:
1297:
1044:
986:
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789:0.478631328575115
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696:0.478631328575115
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531:
510:
508:
480:
426:
389:Andrew M. Gleason
366:
279:
253:
177:
176:
16:(Redirected from
2027:
1820:Chiliagon (1000)
1800:Icositrigon (23)
1779:Octadecagon (18)
1769:Hexadecagon (16)
1673:
1492:
1485:
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1464:
1463:
1436:
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1377:. Archived from
1360:
1351:
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1243:
1234:
1219:
1214:Schläfli symbols
1200:Related polygons
1195:
1080:r = 1 billion km
1069:
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393:angle trisection
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1844:
1788:
1754:Tridecagon (13)
1744:Hendecagon (11)
1732:
1668:
1662:
1633:Right trapezoid
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1375:10.2307/2323624
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1303:
1301:Petrie polygons
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668:
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640:is shown here.
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449:
448:
447:
445:
415:
408:
407:
391:, based on the
355:
348:
347:
317:
288:
255:
234:
233:
212:Schläfli symbol
201:
121:
101:
96:
91:
89:
75:Schläfli symbol
54:Regular polygon
45:
28:
23:
22:
15:
12:
11:
5:
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2012:
2011:
2005:
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1959:Pseudotriangle
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1790:
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1756:
1751:
1749:Dodecagon (12)
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1560:Quadrilaterals
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1443:External links
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1395:
1369:(3): 186â194.
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1307:Petrie polygon
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1280:
1278:Internal angle
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1223:
1208:is a 13-sided
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1179:Numismatic use
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1173:directed edges
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871:unit of length
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800:unit of length
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399:(light blue).
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321:Pierpont prime
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189:triskaidecagon
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128:Internal angle
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111:Symmetry group
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24:
18:Triskaidecagon
14:
13:
10:
9:
6:
4:
3:
2:
2032:
2021:
2018:
2017:
2015:
2000:
1999:Weakly simple
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1939:Infinite skew
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1854:Star polygons
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1840:Apeirogon (â)
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1784:Icosagon (20)
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1621:
1619:
1618:Parallelogram
1616:
1614:
1613:Orthodiagonal
1611:
1609:
1606:
1604:
1601:
1599:
1596:
1594:
1593:Ex-tangential
1591:
1589:
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1579:
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1442:
1435:, p. 81.
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1405:
1399:
1396:
1384:on 2015-12-19
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1269:
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1238:
1233:
1229:
1226:
1222:Tridecagrams
1220:
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1211:
1207:
1199:
1194:
1190:
1189:
1188:
1186:
1178:
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1174:
1170:
1165:
1163:
1159:
1155:
1151:
1147:
1143:
1139:
1134:
1125:symmetries: Z
1124:
1116:
1112:
1104:
1095:
1088:
1086:
1085:
1081:
1073:
1055:
1051:
1047:
1038:
1034:
1031:
1028:
1023:
1019:
1010:
1009:
1005:
989:
980:
974:
971:
967:
962:
957:
953:
947:
943:
934:
925:
909:
905:
901:
898:
890:
889:
862:
859:
850:
846:
843:
840:
835:
831:
822:
821:
817:
791:
788:
785:
781:
776:
771:
767:
761:
757:
754:
751:
748:
745:
742:
739:
730:
721:
695:
692:
689:
682:
678:
677:
671:
662:
656:
652:
645:
641:
639:
635:
616:
613:
608:
603:
599:
594:
586:
581:
578:
572:
568:
565:
560:
554:
548:
540:
536:
533:
528:
525:
519:
515:
512:
505:
500:
497:
494:
489:
486:
482:
477:
473:
470:
464:
460:
457:
454:
431:
428:
419:
416:
404:
400:
398:
394:
390:
387:according to
374:
371:
368:
359:
356:
345:
340:
338:
334:
330:
326:
322:
314:
298:
293:
289:
284:
281:
276:
273:
268:
265:
260:
256:
250:
247:
242:
239:
232:
231:
230:
228:
224:
220:
215:
213:
209:
207:
198:
196:
194:
190:
186:
182:
172:
170:
166:
163:
159:
155:
151:
147:
144:
140:
136:
133:
129:
125:
122:), order 2Ă13
117:
114:
112:
108:
88:
86:
82:
78:
76:
72:
68:
66:
62:
58:
55:
52:
48:
41:
36:
31:
19:
1793:>20 sides
1753:
1728:Decagon (10)
1713:Heptagon (7)
1703:Pentagon (5)
1693:Triangle (3)
1588:Equidiagonal
1457:
1454:"Tridecagon"
1424:
1419:
1398:
1386:. Retrieved
1379:the original
1366:
1362:
1349:
1304:
1210:star polygon
1205:
1203:
1182:
1168:
1166:
1161:
1157:
1153:
1149:
1145:
1141:
1135:
1123:cyclic group
1115:prime number
1102:
1100:
1083:
1079:
1077:
650:
634:straightedge
631:
343:
341:
325:Fermat prime
318:
315:Construction
229:is given by
226:
216:
204:
202:
188:
184:
178:
169:Dual polygon
1989:Star-shaped
1964:Rectilinear
1934:Equilateral
1929:Equiangular
1893:Hendecagram
1737:11â20 sides
1718:Octagon (8)
1708:Hexagon (6)
1683:Monogon (1)
1525:Equilateral
1388:24 December
1206:tridecagram
1138:John Conway
329:constructed
319:As 13 is a
154:equilateral
1994:Tangential
1898:Dodecagram
1676:1â10 sides
1667:By number
1648:Tangential
1628:Right kite
1433:0896894290
1341:References
1333:12-simplex
1310:12-simplex
1294:â13.8462°
323:but not a
208:tridecagon
185:tridecagon
142:Properties
1974:Reinhardt
1883:Enneagram
1873:Heptagram
1863:Pentagram
1830:65537-gon
1688:Digon (2)
1658:Trapezoid
1623:Rectangle
1573:Bicentric
1535:Isosceles
1512:Triangles
1459:MathWorld
1291:â41.5385°
1288:â69.2308°
1285:â96.9231°
1282:â124.615°
1056:∘
1039:μ
1035:−
1032:μ
1024:μ
990:∘
984:¯
958:∘
935:μ
910:∘
899:μ
847:−
792:…
772:∘
758:
752:⋅
746:⋅
614:−
582:−
537:
516:
498:−
474:π
461:
424:¯
364:¯
282:≃
274:π
269:
137:â152.308°
2014:Category
1949:Isotoxal
1944:Isogonal
1888:Decagram
1878:Octagram
1868:Hexagram
1669:of sides
1598:Harmonic
1499:Polygons
1227:Picture
1121:, and 2
1111:symmetry
1089:Symmetry
681:GeoGebra
397:Tomahawk
331:using a
181:geometry
162:isotoxal
158:isogonal
116:Dihedral
65:vertices
1969:Regular
1914:Concave
1907:Classes
1815:257-gon
1638:Rhombus
1578:Crossed
1272:{13/6}
1263:{13/5}
1254:{13/4}
1245:{13/3}
1236:{13/2}
1129:, and Z
638:compass
285:13.1858
223:degrees
219:regular
206:regular
193:polygon
132:degrees
1979:Simple
1924:Cyclic
1919:Convex
1643:Square
1583:Cyclic
1545:Obtuse
1540:Kepler
1431:
1410:
1043:target
981:692307
939:target
855:target
735:target
667:": -->
534:arctan
337:neusis
214:{13}.
150:cyclic
146:Convex
1954:Magic
1550:Right
1530:Ideal
1520:Acute
1382:(PDF)
1359:(PDF)
61:Edges
1984:Skew
1608:Kite
1503:List
1429:ISBN
1408:ISBN
1390:2015
1105:has
1101:The
669:edit
636:and
183:, a
173:Self
79:{13}
63:and
50:Type
1371:doi
1169:g13
1142:r26
1107:Dih
1052:0.0
975:27.
954:360
863:0.0
768:180
755:sin
513:cos
458:cos
266:cot
187:or
179:In
2016::
1456:.
1367:95
1365:.
1361:.
1320:12
1312::
1204:A
1187:.
1175:.
1146:a1
1133:.
1127:13
1109:13
963:13
777:13
617:1.
609:13
587:13
561:13
506:13
495:26
478:13
455:12
432:12
372:12
277:13
248:13
203:A
195:.
160:,
156:,
152:,
148:,
120:13
118:(D
69:13
1505:)
1501:(
1491:e
1484:t
1477:v
1462:.
1392:.
1373::
1318:A
1162:g
1158:i
1154:p
1150:d
1131:1
1119:1
1048:=
1029:=
1020:F
972:=
968:)
948:(
944:=
902:=
875:]
867:[
860:=
851:a
844:a
841:=
836:a
832:F
804:]
796:[
786:=
782:)
762:(
749:2
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731:a
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700:[
693:=
690:a
673:]
604:+
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579:7
573:)
569:1
566:+
555:(
549:3
541:(
529:3
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501:2
490:2
487:=
483:)
471:2
465:(
429:=
420:A
417:O
375:,
369:=
360:A
357:O
299:.
294:2
290:a
261:2
257:a
251:4
243:=
240:A
227:a
134:)
130:(
20:)
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