3198:
3191:
3184:
2806:
3029:
3022:
3015:
3008:
3001:
2992:
2985:
2978:
2971:
280:
2375:
40:
2363:
312:
269:
260:
3315:
2794:
2824:
3293:
3152:
3282:
3409:
3145:
3304:
3131:
3122:
2964:
3395:
3384:
3138:
3115:
3108:
3434:
3423:
3097:
2783:
2582:
1841:
2121:
1984:
2611:
1695:
2261:
1609:
814:
2465:
1436:
894:
719:
1719:
2827:
Symmetries of a regular decagon. Vertices are colored by their symmetry positions. Blue mirrors are drawn through vertices, and purple mirrors are drawn through edges. Gyration orders are given in the center.
2002:
1863:
2778:{\displaystyle {\frac {\overline {E_{1}E_{10}}}{\overline {E_{1}F}}}={\frac {\overline {E_{10}F}}{\overline {E_{1}E_{10}}}}={\frac {R}{a}}={\frac {1+{\sqrt {5}}}{2}}=\Phi \approx 1.618{\text{.}}}
1334:
1170:
2320:
1481:
1255:
596:
1117:
1076:
404:
929:
530:
1204:
2156:
2878:
These 8 symmetries can be seen in 10 distinct symmetries on the decagon, a larger number because the lines of reflections can either pass through vertices or edges.
627:
473:
1614:
1278:
1032:
969:
949:
550:
493:
444:
424:
356:
336:
1511:
1006:
2180:
1516:
2577:{\displaystyle {\frac {\overline {AM}}{\overline {MH}}}={\frac {\overline {AH}}{\overline {AM}}}={\frac {1+{\sqrt {5}}}{2}}=\Phi \approx 1.618{\text{.}}}
727:
3056:-1)/2 parallelograms. In particular this is true for regular polygons with evenly many sides, in which case the parallelograms are all rhombi. For the
3078:
1357:
4261:
2430:
The five corners of the pentagon constitute alternate corners of the decagon. Join these points to the adjacent new points to form the decagon.
1836:{\displaystyle A={\frac {5}{2}}a^{2}\cot \left({\frac {\pi }{10}}\right)={\frac {5}{2}}a^{2}{\sqrt {5+2{\sqrt {5}}}}\simeq 7.694208843\,a^{2}}
3637:
1341:
819:
632:
2402:
to the opposite side of that same circle. Where each line cuts the circle is a vertex of the decagon. In other words,
3591:
2116:{\displaystyle A=5\sin \left({\frac {\pi }{5}}\right)R^{2}={\frac {5}{2}}R^{2}{\sqrt {\frac {5-{\sqrt {5}}}{2}}}\simeq 2.938926261\,R^{2}}
3721:
3532:
3505:
1979:{\displaystyle A=10\tan \left({\frac {\pi }{10}}\right)r^{2}=2r^{2}{\sqrt {5\left(5-2{\sqrt {5}}\right)}}\simeq 3.249196962\,r^{2}}
3197:
120:
110:
92:
4256:
3248:
with equal edge lengths. In 3-dimensions it will be a zig-zag skew decagon and can be seen in the vertices and side edges of a
2423: pentagon, and the two pentagons have in total the vertices of a concentric
102:
3086:
defines the number of solutions as 62, with 2 orientations for the first symmetric form, and 10 orientations for the other 6.
97:
3257:
3214:
128:
115:
3064:=5, and it can be divided into 10 rhombs, with examples shown below. This decomposition can be seen as 10 of 80 faces in a
3231:
with 10 vertices and edges but not existing on the same plane. The interior of such a decagon is not generally defined. A
2936:
decagon, constructed with equal edge lengths, but vertices alternating two different internal angles. These two forms are
1283:
218:
3190:
1126:
3844:
3824:
84:
3183:
4266:
3819:
3776:
3751:
289:
2902:
when reflection lines path through both edges and vertices. Cyclic symmetries in the middle column are labeled as
2276:
3456:
3879:
2343:
1441:
3804:
3319:
3073:
2374:
2805:
2362:
3829:
3714:
3253:
3210:
2162:
is the distance between parallel sides, or the height when the decagon stands on one side as base, or the
3559:
as the edge length and gives the argument of the cotangent as an angle in degrees rather than in radians.
4230:
4170:
3809:
3629:
3341:
2419:
2339:
1209:
1120:
245:
558:
4251:
4114:
3884:
3814:
3756:
3268:
3249:
3240:
3206:
2267:
359:
3028:
3021:
3014:
3007:
3000:
2991:
2984:
2977:
1081:
1040:
4220:
4195:
4165:
4160:
4119:
3834:
3466:
2970:
2403:
171:
369:
4225:
3766:
2879:
2415:
899:
599:
498:
241:
74:
39:
4205:
3799:
3707:
3676:
3633:
3528:
3501:
3495:
3308:
3245:
2836:
1177:
311:
268:
133:
64:
3548:
2129:
3734:
3593:
Euclid's Plane
Geometry, Books IIIâVI, Practically Applied, or Gradations in Euclid, Part II
3522:
3452:
2407:
2167:
1854:
1690:{\displaystyle A_{\Delta }={\frac {a}{2}}\cdot h={\frac {a^{2}}{4}}{\sqrt {5+2{\sqrt {5}}}}}
293:
2909:
Each subgroup symmetry allows one or more degrees of freedom for irregular forms. Only the
605:
451:
279:
4200:
4180:
4175:
4145:
3864:
3839:
3771:
3460:
3349:
2933:
2925:
2439:
Both in the construction with given circumcircle as well as with given side length is the
2411:
259:
235:
179:
175:
60:
53:
1262:
1011:
3314:
240:
has all sides of equal length and each internal angle will always be equal to 144°. Its
4210:
4190:
4155:
4150:
3781:
3761:
3337:
3065:
2890:. The dihedral symmetries are divided depending on whether they pass through vertices (
954:
934:
535:
478:
429:
409:
341:
321:
297:
222:
167:
163:
149:
145:
3640:(Chapter 20, Generalized Schaefli symbols, Types of symmetry of a polygon pp. 275-278)
2823:
1486:
974:
4245:
4185:
4036:
3929:
3849:
3791:
3612:
3345:
2914:
2793:
2256:{\displaystyle d=2a\left(\cos {\tfrac {3\pi }{10}}+\cos {\tfrac {\pi }{10}}\right),}
1604:{\displaystyle h={\sqrt {R^{2}-(a/2)^{2}}}={\frac {a}{2}}{\sqrt {5+2{\sqrt {5}}}}\;}
288:
Decagons often appear in tilings with (partial) 5-fold symmetry. The images show an
4215:
4085:
4041:
4005:
3995:
3990:
3470:
3286:
3281:
3228:
2937:
2856:
2601:
2440:
2335:
2331:
2171:
1990:
186:
3303:
3292:
3048:-gon whose opposite sides are parallel and of equal length) can be dissected into
2928:
decagon constructed by five mirrors which can alternate long and short edges, and
2447:
In the construction with given circumcircle the circular arc around G with radius
809:{\displaystyle m\angle PE_{1}E_{10}=180^{\circ }-2\cdot 72^{\circ }=36^{\circ }\;}
3570:
2588:
In the construction with given side length the circular arc around D with radius
4124:
4031:
4010:
4000:
3572:
Geometric
Construction of the Regular Decagon and Pentagon Inscribed in a Circle
3427:
3399:
3297:
3271:. The polygons on the perimeter of these projections are regular skew decagons.
3151:
3408:
3144:
2882:
labels these by a letter and group order. Full symmetry of the regular form is
1431:{\displaystyle \;R={\frac {2a}{{\sqrt {5}}-1}}={\frac {a}{2}}({\sqrt {5}}+1)\;}
4129:
3985:
3975:
3859:
3413:
3130:
3679:
4104:
4094:
4071:
4061:
4051:
3980:
3889:
3854:
3684:
3388:
2347:
3121:
2963:
3693:
3394:
3383:
3137:
3114:
4109:
4099:
4056:
4015:
3944:
3934:
3924:
3743:
3614:
RegelmĂ€Ăiges
Zehneck, â 3. Section "Formeln, Ist die Seite a gegeben ..."
2398:
Extend a line from each vertex of the pentagon through the center of the
2392:
2351:
2163:
248:
198:
17:
3107:
4066:
4046:
3954:
3949:
3939:
3914:
3869:
3730:
3649:
3041:
3037:
2951:
2940:
of each other and have half the symmetry order of the regular decagon.
1847:
889:{\displaystyle \;m\angle ME_{1}P=72^{\circ }-36^{\circ }=36^{\circ }\;}
714:{\displaystyle m\angle E_{1}E_{10}P=m\angle E_{10}PE_{1}=72^{\circ }\;}
214:
3433:
3422:
3096:
3874:
3438:
3101:
3069:
2399:
3919:
3699:
3164:
3652:, Mathematical recreations and Essays, Thirteenth edition, p.141
2391:
Construct a pentagon in a circle by one of the methods shown in
1706:
3703:
251:, t{5}, a quasiregular decagon alternating two types of edges.
3661:
Coxeter, Regular polytopes, 12.4 Petrie polygon, pp. 223-226.
3553:, Society for Promoting Christian Knowledge, 1850, p. 59
3348:: The number of sides in the Petrie polygon is equal to the
310:
3267:
These can also be seen in these four convex polyhedra with
3082:
3205:
A regular skew decagon is seen as zig-zagging edges of a
2843:, order 20. There are 3 subgroup dihedral symmetries: Dih
2441:
golden ratio dividing a line segment by exterior division
1119:
have equal angles of 36° at the vertex, and so they are
3340:
for many higher-dimensional polytopes, shown in these
3235:
has vertices alternating between two parallel planes.
2947:
2913:
subgroup has no degrees of freedom but can be seen as
2234:
2208:
3473:
with the same vertex positions as the regular decagon
2614:
2468:
2279:
2183:
2132:
2005:
1866:
1722:
1617:
1519:
1489:
1444:
1360:
1286:
1265:
1212:
1180:
1129:
1084:
1043:
1014:
977:
957:
937:
902:
822:
730:
635:
608:
561:
538:
501:
481:
454:
432:
412:
372:
344:
324:
318:
The picture shows a regular decagon with side length
3358:
3273:
4138:
4084:
4024:
3968:
3907:
3898:
3790:
3742:
3275:Orthogonal projections of polyhedra on 5-fold axes
2387:An alternative (but similar) method is as follows:
185:
159:
144:
127:
83:
73:
59:
49:
32:
3596:, London: Simpkin, Marshall,& CO., p. 116
2777:
2576:
2314:
2255:
2150:
2115:
1978:
1835:
1689:
1603:
1505:
1475:
1430:
1329:{\displaystyle \;a={\frac {R}{2}}(-1+{\sqrt {5}})}
1328:
1272:
1249:
1198:
1164:
1111:
1070:
1026:
1000:
963:
943:
923:
888:
808:
713:
621:
590:
544:
524:
487:
467:
438:
418:
398:
350:
330:
3072:. A dissection is based on 10 of 30 faces of the
2458:, whose division corresponds to the golden ratio.
1165:{\displaystyle \;{\frac {a}{R}}={\frac {R-a}{a}}}
3550:The elements of plane and spherical trigonometry
3606:
3604:
1339:So the regular decagon can be constructed with
3715:
3585:
3583:
2406:of a regular pentagon under a
8:
3489:
3487:
2920:The highest symmetry irregular decagons are
2315:{\displaystyle d=a{\sqrt {5+2{\sqrt {5}}}}.}
292:(15th century), an illustration in Kepler's
2811:Decagon with a given side length, animation
3904:
3722:
3708:
3700:
2799:Decagon with given circumcircle, animation
1600:
1427:
1361:
1287:
1246:
1213:
1130:
1108:
1067:
931:is also an isosceles triangle with vertex
920:
903:
885:
823:
805:
710:
587:
244:is {10} and can also be constructed as a
3527:, Cambridge University Press, p. 9,
3380:
3278:
3093:
3090:Regular decagon dissected into 10 rhombi
2770:
2745:
2736:
2723:
2707:
2697:
2677:
2669:
2650:
2633:
2623:
2615:
2613:
2569:
2544:
2535:
2502:
2469:
2467:
2300:
2289:
2278:
2233:
2207:
2182:
2131:
2107:
2102:
2082:
2072:
2066:
2052:
2043:
2025:
2004:
1970:
1965:
1945:
1926:
1920:
1904:
1886:
1865:
1827:
1822:
1807:
1796:
1790:
1776:
1759:
1743:
1729:
1721:
1678:
1667:
1656:
1650:
1631:
1622:
1616:
1591:
1580:
1570:
1559:
1547:
1532:
1526:
1518:
1496:
1488:
1472:
1463:
1453:
1448:
1443:
1411:
1398:
1379:
1368:
1359:
1316:
1294:
1285:
1269:
1264:
1231:
1218:
1211:
1179:
1144:
1131:
1128:
1102:
1092:
1083:
1058:
1048:
1042:
1013:
989:
984:
976:
956:
936:
908:
901:
879:
866:
853:
837:
821:
799:
786:
767:
754:
744:
729:
704:
691:
678:
656:
646:
634:
613:
607:
577:
567:
562:
560:
537:
513:
508:
500:
480:
459:
453:
431:
411:
387:
377:
371:
343:
323:
3497:The A to Z of Mathematics: A Basic Guide
3088:
2822:
3483:
2338:, it follows that a regular decagon is
1476:{\displaystyle \Delta \,E_{10}E_{1}M\,}
3694:Definition and properties of a decagon
3500:, John Wiley & Sons, p. 146,
2443:the determining construction element.
406:has two equally long legs with length
29:
1174:Multiplication with the denominators
7:
2600:, whose division corresponds to the
1709:of a regular decagon of side length
3632:, (2008) The Symmetries of Things,
2906:for their central gyration orders.
2761:
2560:
1623:
1445:
1259:This equation for the side length
1250:{\displaystyle \;a^{2}=R^{2}-aR\;}
827:
734:
671:
639:
25:
1206:leads to the quadratic equation:
3432:
3421:
3407:
3393:
3382:
3313:
3302:
3291:
3280:
3196:
3189:
3182:
3166:3 regular skew zig-zag decagons
3150:
3143:
3136:
3129:
3120:
3113:
3106:
3095:
3027:
3020:
3013:
3006:
2999:
2990:
2983:
2976:
2969:
2962:
2804:
2792:
2373:
2361:
591:{\displaystyle {E_{10}E_{1}P}\;}
552:(not designated in the picture).
278:
267:
258:
217:or 10-gon. The total sum of the
118:
113:
108:
100:
95:
90:
38:
4262:Polygons by the number of sides
3628:John H. Conway, Heidi Burgiel,
3575:, The Open Court Publishing Co.
1611:and the triangle has the area:
3494:Sidebotham, Thomas H. (2003),
3258:pentagrammic crossed-antiprism
3215:pentagrammic crossed-antiprism
1556:
1541:
1500:
1490:
1424:
1408:
1323:
1304:
1112:{\displaystyle PE_{10}E_{1}\;}
1071:{\displaystyle E_{10}E_{1}M\;}
995:
978:
519:
502:
1:
3619:. Retrieved 10 February 2016.
3598:. Retrieved 10 February 2016.
3555:. Note that this source uses
3521:Wenninger, Magnus J. (1974),
213:"ten angles") is a ten-sided
3356:, for each symmetry family.
2997:
2960:
2714:
2687:
2660:
2640:
2526:
2513:
2493:
2480:
951:. The length of its legs is
399:{\displaystyle E_{10}E_{1}M}
2886:and no symmetry is labeled
2435:The golden ratio in decagon
1280:has one positive solution:
924:{\displaystyle \;E_{1}MP\;}
525:{\displaystyle ]M\,E_{10}[}
4283:
3696:With interactive animation
2410:with respect of
2126:An alternative formula is
3569:Ludlow, Henry H. (1904),
3457:centered decagonal number
3373:
3367:
3204:
2956:
2898:for perpendiculars), and
290:Islamic geometric pattern
37:
3068:projection plane of the
2894:for diagonal) or edges (
2380:Construction of pentagon
2344:compass and straightedge
1199:{\displaystyle R,a>0}
1037:The isosceles triangles
3611:Köller, JĂŒrgen (2005),
3320:Rhombic triacontahedron
3264:, symmetry, order 20.
3074:rhombic triacontahedron
2393:constructing a pentagon
2368:Construction of decagon
2151:{\displaystyle A=2.5da}
1438:and the base height of
426:and a base with length
85:CoxeterâDynkin diagrams
4257:Constructible polygons
3463:modeled on the decagon
3342:orthogonal projections
3254:pentagrammic antiprism
3211:pentagrammic antiprism
2828:
2779:
2578:
2316:
2266:and it can be written
2257:
2152:
2117:
1980:
1837:
1691:
1605:
1507:
1477:
1432:
1330:
1274:
1251:
1200:
1166:
1113:
1072:
1028:
1002:
965:
945:
925:
890:
810:
715:
623:
592:
546:
526:
489:
469:
440:
420:
400:
352:
332:
315:
3630:Chaim Goodman-Strauss
3590:Green, Henry (1861),
2826:
2780:
2592:produces the segment
2579:
2454:produces the segment
2408:point reflection
2317:
2258:
2153:
2118:
1981:
1838:
1692:
1606:
1508:
1478:
1433:
1331:
1275:
1252:
1201:
1167:
1114:
1073:
1029:
1003:
966:
946:
926:
891:
811:
716:
629:and with base angles
624:
622:{\displaystyle E_{1}}
593:
547:
527:
490:
470:
468:{\displaystyle E_{1}}
441:
421:
401:
353:
333:
314:
205:(from the Greek ÎŽÎÎșα
3955:Nonagon/Enneagon (9)
3885:Tangential trapezoid
3334:regular skew decagon
3269:icosahedral symmetry
3250:pentagonal antiprism
3241:regular skew decagon
3233:skew zig-zag decagon
3207:pentagonal antiprism
2957:40 rhomb dissection
2612:
2466:
2425:regular decagon
2277:
2181:
2130:
2003:
1864:
1720:
1615:
1517:
1487:
1483:(i.e. the length of
1442:
1358:
1284:
1263:
1210:
1178:
1127:
1082:
1041:
1012:
975:
955:
935:
900:
820:
728:
633:
606:
559:
536:
499:
479:
452:
430:
410:
370:
360:circumscribed circle
342:
322:
27:Shape with ten sides
4067:Megagon (1,000,000)
3835:Isosceles trapezoid
3276:
3167:
3091:
1349:Further conclusions
1273:{\displaystyle a\,}
1027:{\displaystyle R-a}
971:, so the length of
4037:Icositetragon (24)
3677:Weisstein, Eric W.
3274:
3165:
3089:
3040:states that every
2829:
2775:
2574:
2312:
2253:
2243:
2222:
2148:
2113:
1976:
1833:
1687:
1601:
1503:
1473:
1428:
1326:
1270:
1247:
1196:
1162:
1109:
1068:
1024:
998:
961:
941:
921:
886:
806:
711:
619:
600:isosceles triangle
588:
542:
522:
485:
465:
448:The circle around
436:
416:
396:
348:
328:
316:
225:decagon is 1440°.
4267:Elementary shapes
4239:
4238:
4080:
4079:
4057:Myriagon (10,000)
4042:Triacontagon (30)
4006:Heptadecagon (17)
3996:Pentadecagon (15)
3991:Tetradecagon (14)
3930:Quadrilateral (4)
3800:Antiparallelogram
3638:978-1-56881-220-5
3524:Polyhedron Models
3444:
3443:
3325:
3324:
3309:Icosidodecahedron
3246:vertex-transitive
3221:
3220:
3158:
3157:
3035:
3034:
2773:
2756:
2750:
2731:
2718:
2717:
2690:
2664:
2663:
2643:
2572:
2555:
2549:
2530:
2529:
2516:
2497:
2496:
2483:
2330:As 10 = 2 Ă 5, a
2307:
2305:
2242:
2221:
2166:of the decagon's
2094:
2093:
2087:
2060:
2033:
1957:
1950:
1894:
1814:
1812:
1784:
1767:
1737:
1685:
1683:
1665:
1639:
1598:
1596:
1578:
1565:
1416:
1406:
1393:
1384:
1342:ruler and compass
1321:
1302:
1160:
1139:
964:{\displaystyle a}
944:{\displaystyle P}
555:Now the triangle
545:{\displaystyle P}
488:{\displaystyle a}
439:{\displaystyle a}
419:{\displaystyle R}
351:{\displaystyle R}
331:{\displaystyle a}
195:
194:
44:A regular decagon
16:(Redirected from
4274:
4052:Chiliagon (1000)
4032:Icositrigon (23)
4011:Octadecagon (18)
4001:Hexadecagon (16)
3905:
3724:
3717:
3710:
3701:
3690:
3689:
3662:
3659:
3653:
3647:
3641:
3626:
3620:
3618:
3608:
3599:
3597:
3587:
3578:
3576:
3566:
3560:
3554:
3545:
3539:
3537:
3518:
3512:
3510:
3491:
3461:figurate numbers
3453:Decagonal number
3436:
3425:
3411:
3397:
3386:
3359:
3317:
3306:
3295:
3284:
3277:
3200:
3193:
3186:
3168:
3154:
3147:
3140:
3133:
3124:
3117:
3110:
3099:
3092:
3085:
3031:
3024:
3017:
3010:
3003:
2994:
2987:
2980:
2973:
2966:
2948:
2808:
2796:
2784:
2782:
2781:
2776:
2774:
2771:
2757:
2752:
2751:
2746:
2737:
2732:
2724:
2719:
2713:
2712:
2711:
2702:
2701:
2691:
2686:
2682:
2681:
2671:
2670:
2665:
2659:
2655:
2654:
2644:
2639:
2638:
2637:
2628:
2627:
2617:
2616:
2599:
2591:
2583:
2581:
2580:
2575:
2573:
2570:
2556:
2551:
2550:
2545:
2536:
2531:
2525:
2517:
2512:
2504:
2503:
2498:
2492:
2484:
2479:
2471:
2470:
2457:
2453:
2377:
2365:
2346:, or by an edge-
2321:
2319:
2318:
2313:
2308:
2306:
2301:
2290:
2262:
2260:
2259:
2254:
2249:
2245:
2244:
2235:
2223:
2217:
2209:
2168:inscribed circle
2157:
2155:
2154:
2149:
2122:
2120:
2119:
2114:
2112:
2111:
2095:
2089:
2088:
2083:
2074:
2073:
2071:
2070:
2061:
2053:
2048:
2047:
2038:
2034:
2026:
1989:In terms of the
1985:
1983:
1982:
1977:
1975:
1974:
1958:
1956:
1952:
1951:
1946:
1927:
1925:
1924:
1909:
1908:
1899:
1895:
1887:
1857:), the area is:
1855:inscribed figure
1846:In terms of the
1842:
1840:
1839:
1834:
1832:
1831:
1815:
1813:
1808:
1797:
1795:
1794:
1785:
1777:
1772:
1768:
1760:
1748:
1747:
1738:
1730:
1696:
1694:
1693:
1688:
1686:
1684:
1679:
1668:
1666:
1661:
1660:
1651:
1640:
1632:
1627:
1626:
1610:
1608:
1607:
1602:
1599:
1597:
1592:
1581:
1579:
1571:
1566:
1564:
1563:
1551:
1537:
1536:
1527:
1512:
1510:
1509:
1506:{\displaystyle }
1504:
1482:
1480:
1479:
1474:
1468:
1467:
1458:
1457:
1437:
1435:
1434:
1429:
1417:
1412:
1407:
1399:
1394:
1392:
1385:
1380:
1377:
1369:
1335:
1333:
1332:
1327:
1322:
1317:
1303:
1295:
1279:
1277:
1276:
1271:
1256:
1254:
1253:
1248:
1236:
1235:
1223:
1222:
1205:
1203:
1202:
1197:
1171:
1169:
1168:
1163:
1161:
1156:
1145:
1140:
1132:
1118:
1116:
1115:
1110:
1107:
1106:
1097:
1096:
1077:
1075:
1074:
1069:
1063:
1062:
1053:
1052:
1033:
1031:
1030:
1025:
1007:
1005:
1004:
1001:{\displaystyle }
999:
994:
993:
970:
968:
967:
962:
950:
948:
947:
942:
930:
928:
927:
922:
913:
912:
895:
893:
892:
887:
884:
883:
871:
870:
858:
857:
842:
841:
815:
813:
812:
807:
804:
803:
791:
790:
772:
771:
759:
758:
749:
748:
720:
718:
717:
712:
709:
708:
696:
695:
683:
682:
661:
660:
651:
650:
628:
626:
625:
620:
618:
617:
597:
595:
594:
589:
586:
582:
581:
572:
571:
551:
549:
548:
543:
531:
529:
528:
523:
518:
517:
494:
492:
491:
486:
474:
472:
471:
466:
464:
463:
445:
443:
442:
437:
425:
423:
422:
417:
405:
403:
402:
397:
392:
391:
382:
381:
357:
355:
354:
349:
337:
335:
334:
329:
294:Harmonices Mundi
282:
271:
262:
123:
122:
121:
117:
116:
112:
111:
105:
104:
103:
99:
98:
94:
93:
42:
30:
21:
4282:
4281:
4277:
4276:
4275:
4273:
4272:
4271:
4242:
4241:
4240:
4235:
4134:
4088:
4076:
4020:
3986:Tridecagon (13)
3976:Hendecagon (11)
3964:
3900:
3894:
3865:Right trapezoid
3786:
3738:
3728:
3675:
3674:
3671:
3666:
3665:
3660:
3656:
3648:
3644:
3627:
3623:
3610:
3609:
3602:
3589:
3588:
3581:
3568:
3567:
3563:
3547:
3546:
3542:
3535:
3520:
3519:
3515:
3508:
3493:
3492:
3485:
3480:
3449:
3437:
3426:
3417:
3412:
3403:
3398:
3387:
3377:
3371:
3365:
3330:
3328:Petrie polygons
3318:
3307:
3296:
3285:
3263:
3260:with the same D
3163:
3100:
3077:
3058:regular decagon
2946:
2874:
2870:
2866:
2862:
2854:
2850:
2846:
2840:
2833:regular decagon
2821:
2816:
2815:
2814:
2813:
2812:
2809:
2801:
2800:
2797:
2738:
2703:
2693:
2692:
2673:
2672:
2646:
2645:
2629:
2619:
2618:
2610:
2609:
2597:
2593:
2589:
2537:
2518:
2505:
2485:
2472:
2464:
2463:
2455:
2452:
2448:
2437:
2412:its center
2385:
2384:
2383:
2382:
2381:
2378:
2370:
2369:
2366:
2328:
2275:
2274:
2210:
2200:
2196:
2179:
2178:
2128:
2127:
2103:
2075:
2062:
2039:
2021:
2001:
2000:
1996:, the area is:
1966:
1935:
1931:
1916:
1900:
1882:
1862:
1861:
1823:
1786:
1755:
1739:
1718:
1717:
1703:
1652:
1618:
1613:
1612:
1555:
1528:
1515:
1514:
1485:
1484:
1459:
1449:
1440:
1439:
1378:
1370:
1356:
1355:
1282:
1281:
1261:
1260:
1227:
1214:
1208:
1207:
1176:
1175:
1146:
1125:
1124:
1098:
1088:
1080:
1079:
1054:
1044:
1039:
1038:
1010:
1009:
985:
973:
972:
953:
952:
933:
932:
904:
898:
897:
875:
862:
849:
833:
818:
817:
795:
782:
763:
750:
740:
726:
725:
700:
687:
674:
652:
642:
631:
630:
609:
604:
603:
573:
563:
557:
556:
534:
533:
509:
497:
496:
477:
476:
455:
450:
449:
428:
427:
408:
407:
383:
373:
368:
367:
340:
339:
320:
319:
309:
304:
303:
302:
301:
285:
284:
283:
274:
273:
272:
264:
263:
242:SchlÀfli symbol
231:
229:Regular decagon
219:interior angles
139:
119:
114:
109:
107:
106:
101:
96:
91:
89:
75:SchlÀfli symbol
54:Regular polygon
45:
33:Regular decagon
28:
23:
22:
15:
12:
11:
5:
4280:
4278:
4270:
4269:
4264:
4259:
4254:
4244:
4243:
4237:
4236:
4234:
4233:
4228:
4223:
4218:
4213:
4208:
4203:
4198:
4193:
4191:Pseudotriangle
4188:
4183:
4178:
4173:
4168:
4163:
4158:
4153:
4148:
4142:
4140:
4136:
4135:
4133:
4132:
4127:
4122:
4117:
4112:
4107:
4102:
4097:
4091:
4089:
4082:
4081:
4078:
4077:
4075:
4074:
4069:
4064:
4059:
4054:
4049:
4044:
4039:
4034:
4028:
4026:
4022:
4021:
4019:
4018:
4013:
4008:
4003:
3998:
3993:
3988:
3983:
3981:Dodecagon (12)
3978:
3972:
3970:
3966:
3965:
3963:
3962:
3957:
3952:
3947:
3942:
3937:
3932:
3927:
3922:
3917:
3911:
3909:
3902:
3896:
3895:
3893:
3892:
3887:
3882:
3877:
3872:
3867:
3862:
3857:
3852:
3847:
3842:
3837:
3832:
3827:
3822:
3817:
3812:
3807:
3802:
3796:
3794:
3792:Quadrilaterals
3788:
3787:
3785:
3784:
3779:
3774:
3769:
3764:
3759:
3754:
3748:
3746:
3740:
3739:
3729:
3727:
3726:
3719:
3712:
3704:
3698:
3697:
3691:
3670:
3669:External links
3667:
3664:
3663:
3654:
3642:
3621:
3600:
3579:
3561:
3540:
3533:
3513:
3506:
3482:
3481:
3479:
3476:
3475:
3474:
3464:
3448:
3445:
3442:
3441:
3430:
3419:
3415:
3405:
3401:
3391:
3379:
3378:
3375:
3372:
3369:
3366:
3363:
3350:Coxeter number
3346:Coxeter planes
3338:Petrie polygon
3329:
3326:
3323:
3322:
3311:
3300:
3289:
3261:
3219:
3218:
3202:
3201:
3194:
3187:
3179:
3178:
3175:
3172:
3162:
3159:
3156:
3155:
3148:
3141:
3134:
3126:
3125:
3118:
3111:
3104:
3066:Petrie polygon
3033:
3032:
3025:
3018:
3011:
3004:
2996:
2995:
2988:
2981:
2974:
2967:
2959:
2958:
2955:
2945:
2942:
2915:directed edges
2872:
2868:
2864:
2860:
2852:
2848:
2844:
2838:
2820:
2817:
2810:
2803:
2802:
2798:
2791:
2790:
2789:
2788:
2787:
2786:
2785:
2769:
2766:
2763:
2760:
2755:
2749:
2744:
2741:
2735:
2730:
2727:
2722:
2716:
2710:
2706:
2700:
2696:
2689:
2685:
2680:
2676:
2668:
2662:
2658:
2653:
2649:
2642:
2636:
2632:
2626:
2622:
2606:
2605:
2595:
2585:
2584:
2568:
2565:
2562:
2559:
2554:
2548:
2543:
2540:
2534:
2528:
2524:
2521:
2515:
2511:
2508:
2501:
2495:
2491:
2488:
2482:
2478:
2475:
2460:
2459:
2450:
2436:
2433:
2432:
2431:
2428:
2404:the image
2396:
2379:
2372:
2371:
2367:
2360:
2359:
2358:
2357:
2356:
2327:
2324:
2323:
2322:
2311:
2304:
2299:
2296:
2293:
2288:
2285:
2282:
2264:
2263:
2252:
2248:
2241:
2238:
2232:
2229:
2226:
2220:
2216:
2213:
2206:
2203:
2199:
2195:
2192:
2189:
2186:
2147:
2144:
2141:
2138:
2135:
2124:
2123:
2110:
2106:
2101:
2098:
2092:
2086:
2081:
2078:
2069:
2065:
2059:
2056:
2051:
2046:
2042:
2037:
2032:
2029:
2024:
2020:
2017:
2014:
2011:
2008:
1987:
1986:
1973:
1969:
1964:
1961:
1955:
1949:
1944:
1941:
1938:
1934:
1930:
1923:
1919:
1915:
1912:
1907:
1903:
1898:
1893:
1890:
1885:
1881:
1878:
1875:
1872:
1869:
1844:
1843:
1830:
1826:
1821:
1818:
1811:
1806:
1803:
1800:
1793:
1789:
1783:
1780:
1775:
1771:
1766:
1763:
1758:
1754:
1751:
1746:
1742:
1736:
1733:
1728:
1725:
1702:
1699:
1682:
1677:
1674:
1671:
1664:
1659:
1655:
1649:
1646:
1643:
1638:
1635:
1630:
1625:
1621:
1595:
1590:
1587:
1584:
1577:
1574:
1569:
1562:
1558:
1554:
1550:
1546:
1543:
1540:
1535:
1531:
1525:
1522:
1502:
1499:
1495:
1492:
1471:
1466:
1462:
1456:
1452:
1447:
1426:
1423:
1420:
1415:
1410:
1405:
1402:
1397:
1391:
1388:
1383:
1376:
1373:
1367:
1364:
1353:
1352:
1350:
1337:
1336:
1325:
1320:
1315:
1312:
1309:
1306:
1301:
1298:
1293:
1290:
1268:
1257:
1245:
1242:
1239:
1234:
1230:
1226:
1221:
1217:
1195:
1192:
1189:
1186:
1183:
1172:
1159:
1155:
1152:
1149:
1143:
1138:
1135:
1105:
1101:
1095:
1091:
1087:
1066:
1061:
1057:
1051:
1047:
1035:
1023:
1020:
1017:
997:
992:
988:
983:
980:
960:
940:
919:
916:
911:
907:
882:
878:
874:
869:
865:
861:
856:
852:
848:
845:
840:
836:
832:
829:
826:
802:
798:
794:
789:
785:
781:
778:
775:
770:
766:
762:
757:
753:
747:
743:
739:
736:
733:
722:
707:
703:
699:
694:
690:
686:
681:
677:
673:
670:
667:
664:
659:
655:
649:
645:
641:
638:
616:
612:
585:
580:
576:
570:
566:
553:
541:
521:
516:
512:
507:
504:
484:
462:
458:
446:
435:
415:
395:
390:
386:
380:
376:
347:
327:
308:
305:
298:Penrose tiling
287:
286:
277:
276:
275:
266:
265:
257:
256:
255:
254:
253:
230:
227:
193:
192:
189:
183:
182:
161:
157:
156:
153:
146:Internal angle
142:
141:
137:
131:
129:Symmetry group
125:
124:
87:
81:
80:
77:
71:
70:
67:
57:
56:
51:
47:
46:
43:
35:
34:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4279:
4268:
4265:
4263:
4260:
4258:
4255:
4253:
4250:
4249:
4247:
4232:
4231:Weakly simple
4229:
4227:
4224:
4222:
4219:
4217:
4214:
4212:
4209:
4207:
4204:
4202:
4199:
4197:
4194:
4192:
4189:
4187:
4184:
4182:
4179:
4177:
4174:
4172:
4171:Infinite skew
4169:
4167:
4164:
4162:
4159:
4157:
4154:
4152:
4149:
4147:
4144:
4143:
4141:
4137:
4131:
4128:
4126:
4123:
4121:
4118:
4116:
4113:
4111:
4108:
4106:
4103:
4101:
4098:
4096:
4093:
4092:
4090:
4087:
4086:Star polygons
4083:
4073:
4072:Apeirogon (â)
4070:
4068:
4065:
4063:
4060:
4058:
4055:
4053:
4050:
4048:
4045:
4043:
4040:
4038:
4035:
4033:
4030:
4029:
4027:
4023:
4017:
4016:Icosagon (20)
4014:
4012:
4009:
4007:
4004:
4002:
3999:
3997:
3994:
3992:
3989:
3987:
3984:
3982:
3979:
3977:
3974:
3973:
3971:
3967:
3961:
3958:
3956:
3953:
3951:
3948:
3946:
3943:
3941:
3938:
3936:
3933:
3931:
3928:
3926:
3923:
3921:
3918:
3916:
3913:
3912:
3910:
3906:
3903:
3897:
3891:
3888:
3886:
3883:
3881:
3878:
3876:
3873:
3871:
3868:
3866:
3863:
3861:
3858:
3856:
3853:
3851:
3850:Parallelogram
3848:
3846:
3845:Orthodiagonal
3843:
3841:
3838:
3836:
3833:
3831:
3828:
3826:
3825:Ex-tangential
3823:
3821:
3818:
3816:
3813:
3811:
3808:
3806:
3803:
3801:
3798:
3797:
3795:
3793:
3789:
3783:
3780:
3778:
3775:
3773:
3770:
3768:
3765:
3763:
3760:
3758:
3755:
3753:
3750:
3749:
3747:
3745:
3741:
3736:
3732:
3725:
3720:
3718:
3713:
3711:
3706:
3705:
3702:
3695:
3692:
3687:
3686:
3681:
3678:
3673:
3672:
3668:
3658:
3655:
3651:
3646:
3643:
3639:
3635:
3631:
3625:
3622:
3616:
3615:
3607:
3605:
3601:
3595:
3594:
3586:
3584:
3580:
3574:
3573:
3565:
3562:
3558:
3552:
3551:
3544:
3541:
3536:
3534:9780521098595
3530:
3526:
3525:
3517:
3514:
3509:
3507:9780471461630
3503:
3499:
3498:
3490:
3488:
3484:
3477:
3472:
3468:
3465:
3462:
3458:
3454:
3451:
3450:
3446:
3440:
3435:
3431:
3429:
3424:
3420:
3418:
3410:
3406:
3404:
3396:
3392:
3390:
3385:
3381:
3361:
3360:
3357:
3355:
3351:
3347:
3343:
3339:
3335:
3327:
3321:
3316:
3312:
3310:
3305:
3301:
3299:
3294:
3290:
3288:
3283:
3279:
3272:
3270:
3265:
3259:
3255:
3251:
3247:
3243:
3242:
3236:
3234:
3230:
3226:
3216:
3212:
3208:
3203:
3199:
3195:
3192:
3188:
3185:
3181:
3180:
3176:
3173:
3170:
3169:
3160:
3153:
3149:
3146:
3142:
3139:
3135:
3132:
3128:
3127:
3123:
3119:
3116:
3112:
3109:
3105:
3103:
3098:
3094:
3087:
3084:
3080:
3075:
3071:
3067:
3063:
3059:
3055:
3051:
3047:
3043:
3039:
3030:
3026:
3023:
3019:
3016:
3012:
3009:
3005:
3002:
2998:
2993:
2989:
2986:
2982:
2979:
2975:
2972:
2968:
2965:
2961:
2953:
2950:
2949:
2943:
2941:
2939:
2935:
2931:
2927:
2923:
2918:
2916:
2912:
2907:
2905:
2901:
2897:
2893:
2889:
2885:
2881:
2876:
2859:symmetries: Z
2858:
2842:
2834:
2825:
2818:
2807:
2795:
2767:
2764:
2758:
2753:
2747:
2742:
2739:
2733:
2728:
2725:
2720:
2708:
2704:
2698:
2694:
2683:
2678:
2674:
2666:
2656:
2651:
2647:
2634:
2630:
2624:
2620:
2608:
2607:
2603:
2587:
2586:
2566:
2563:
2557:
2552:
2546:
2541:
2538:
2532:
2522:
2519:
2509:
2506:
2499:
2489:
2486:
2476:
2473:
2462:
2461:
2446:
2445:
2444:
2442:
2434:
2429:
2426:
2422:
2421:
2417:
2413:
2409:
2405:
2401:
2397:
2394:
2390:
2389:
2388:
2376:
2364:
2355:
2353:
2350:of a regular
2349:
2345:
2341:
2340:constructible
2337:
2333:
2325:
2309:
2302:
2297:
2294:
2291:
2286:
2283:
2280:
2273:
2272:
2271:
2269:
2268:algebraically
2250:
2246:
2239:
2236:
2230:
2227:
2224:
2218:
2214:
2211:
2204:
2201:
2197:
2193:
2190:
2187:
2184:
2177:
2176:
2175:
2173:
2169:
2165:
2161:
2145:
2142:
2139:
2136:
2133:
2108:
2104:
2099:
2096:
2090:
2084:
2079:
2076:
2067:
2063:
2057:
2054:
2049:
2044:
2040:
2035:
2030:
2027:
2022:
2018:
2015:
2012:
2009:
2006:
1999:
1998:
1997:
1995:
1992:
1971:
1967:
1962:
1959:
1953:
1947:
1942:
1939:
1936:
1932:
1928:
1921:
1917:
1913:
1910:
1905:
1901:
1896:
1891:
1888:
1883:
1879:
1876:
1873:
1870:
1867:
1860:
1859:
1858:
1856:
1852:
1849:
1828:
1824:
1819:
1816:
1809:
1804:
1801:
1798:
1791:
1787:
1781:
1778:
1773:
1769:
1764:
1761:
1756:
1752:
1749:
1744:
1740:
1734:
1731:
1726:
1723:
1716:
1715:
1714:
1713:is given by:
1712:
1708:
1700:
1698:
1680:
1675:
1672:
1669:
1662:
1657:
1653:
1647:
1644:
1641:
1636:
1633:
1628:
1619:
1593:
1588:
1585:
1582:
1575:
1572:
1567:
1560:
1552:
1548:
1544:
1538:
1533:
1529:
1523:
1520:
1497:
1493:
1469:
1464:
1460:
1454:
1450:
1421:
1418:
1413:
1403:
1400:
1395:
1389:
1386:
1381:
1374:
1371:
1365:
1362:
1351:
1348:
1347:
1346:
1344:
1343:
1318:
1313:
1310:
1307:
1299:
1296:
1291:
1288:
1266:
1258:
1243:
1240:
1237:
1232:
1228:
1224:
1219:
1215:
1193:
1190:
1187:
1184:
1181:
1173:
1157:
1153:
1150:
1147:
1141:
1136:
1133:
1122:
1103:
1099:
1093:
1089:
1085:
1064:
1059:
1055:
1049:
1045:
1036:
1021:
1018:
1015:
990:
986:
981:
958:
938:
917:
914:
909:
905:
880:
876:
872:
867:
863:
859:
854:
850:
846:
843:
838:
834:
830:
824:
800:
796:
792:
787:
783:
779:
776:
773:
768:
764:
760:
755:
751:
745:
741:
737:
731:
723:
705:
701:
697:
692:
688:
684:
679:
675:
668:
665:
662:
657:
653:
647:
643:
636:
614:
610:
601:
583:
578:
574:
568:
564:
554:
539:
514:
510:
505:
482:
460:
456:
447:
433:
413:
393:
388:
384:
378:
374:
366:The triangle
365:
364:
363:
361:
345:
325:
313:
306:
299:
296:(1619) and a
295:
291:
281:
270:
261:
252:
250:
247:
243:
239:
237:
228:
226:
224:
220:
216:
212:
208:
204:
200:
190:
188:
184:
181:
177:
173:
169:
165:
162:
158:
154:
151:
147:
143:
140:), order 2Ă10
135:
132:
130:
126:
88:
86:
82:
78:
76:
72:
68:
66:
62:
58:
55:
52:
48:
41:
36:
31:
19:
4025:>20 sides
3960:Decagon (10)
3959:
3945:Heptagon (7)
3935:Pentagon (5)
3925:Triangle (3)
3820:Equidiagonal
3683:
3657:
3645:
3624:
3613:
3592:
3571:
3564:
3556:
3549:
3543:
3523:
3516:
3496:
3471:star polygon
3353:
3333:
3331:
3287:Dodecahedron
3266:
3239:
3237:
3232:
3229:skew polygon
3225:skew decagon
3224:
3222:
3161:Skew decagon
3061:
3057:
3053:
3049:
3045:
3036:
2929:
2921:
2919:
2910:
2908:
2903:
2899:
2895:
2891:
2887:
2883:
2877:
2857:cyclic group
2832:
2830:
2602:golden ratio
2438:
2424:
2418:
2386:
2336:Fermat prime
2332:power of two
2329:
2326:Construction
2265:
2172:trigonometry
2170:. By simple
2159:
2125:
1993:
1991:circumradius
1988:
1850:
1845:
1710:
1704:
1354:
1340:
1338:
602:with vertex
475:with radius
317:
234:
232:
210:
206:
202:
196:
187:Dual polygon
4252:10 (number)
4221:Star-shaped
4196:Rectilinear
4166:Equilateral
4161:Equiangular
4125:Hendecagram
3969:11â20 sides
3950:Octagon (8)
3940:Hexagon (6)
3915:Monogon (1)
3757:Equilateral
3617:(in German)
3428:5-orthoplex
3344:in various
3298:Icosahedron
3076:. The list
2954:projection
2880:John Conway
2100:2.938926261
1963:3.249196962
1820:7.694208843
532:in a point
495:intersects
338:and radius
307:Side length
172:equilateral
4246:Categories
4226:Tangential
4130:Dodecagram
3908:1â10 sides
3899:By number
3880:Tangential
3860:Right kite
3478:References
3177:{5/3}#{ }
3174:{5/2}#{ }
2944:Dissection
2416:concentric
2414:is a
1853:(see also
896:and hence
724:Therefore
209:and ÎłÏÎœÎŻÎ±
160:Properties
79:{10}, t{5}
4206:Reinhardt
4115:Enneagram
4105:Heptagram
4095:Pentagram
4062:65537-gon
3920:Digon (2)
3890:Trapezoid
3855:Rectangle
3805:Bicentric
3767:Isosceles
3744:Triangles
3685:MathWorld
3680:"Decagon"
3389:9-simplex
2851:, and Dih
2765:≈
2762:Φ
2715:¯
2688:¯
2661:¯
2641:¯
2564:≈
2561:Φ
2527:¯
2514:¯
2494:¯
2481:¯
2420:congruent
2348:bisection
2237:π
2231:
2215:π
2205:
2097:≃
2080:−
2028:π
2019:
1960:≃
1940:−
1889:π
1880:
1817:≃
1762:π
1753:
1642:⋅
1624:Δ
1539:−
1446:Δ
1387:−
1308:−
1238:−
1151:−
1123:, hence:
1019:−
881:∘
868:∘
860:−
855:∘
828:∠
801:∘
788:∘
780:⋅
774:−
769:∘
735:∠
706:∘
672:∠
640:∠
246:truncated
18:Decagonal
4181:Isotoxal
4176:Isogonal
4120:Decagram
4110:Octagram
4100:Hexagram
3901:of sides
3830:Harmonic
3731:Polygons
3467:Decagram
3447:See also
3213:, and a
3171:{5}#{ }
2934:isotoxal
2926:isogonal
2855:, and 4
2841:symmetry
2819:Symmetry
2352:pentagon
2334:times a
2164:diameter
249:pentagon
199:geometry
180:isotoxal
176:isogonal
134:Dihedral
65:vertices
4201:Regular
4146:Concave
4139:Classes
4047:257-gon
3870:Rhombus
3810:Crossed
3650:Coxeter
3336:is the
3083:A006245
3081::
3042:zonogon
3038:Coxeter
2952:10-cube
2871:, and Z
1848:apothem
1121:similar
358:of the
238:decagon
236:regular
215:polygon
203:decagon
150:degrees
4211:Simple
4156:Cyclic
4151:Convex
3875:Square
3815:Cyclic
3777:Obtuse
3772:Kepler
3636:
3531:
3504:
3439:5-cube
3256:, and
3102:5-cube
3070:5-cube
2400:circle
2342:using
2158:where
598:is an
223:simple
211:gonĂa,
168:cyclic
164:Convex
4186:Magic
3782:Right
3762:Ideal
3752:Acute
3227:is a
2938:duals
2932:, an
2924:, an
2847:, Dih
2768:1.618
2567:1.618
1513:) is
816:. So
221:of a
61:Edges
4216:Skew
3840:Kite
3735:List
3634:ISBN
3529:ISBN
3502:ISBN
3469:, a
3455:and
3332:The
3209:, a
3079:OEIS
3044:(a 2
2835:has
2831:The
1707:area
1705:The
1701:Area
1191:>
1078:and
207:déka
201:, a
191:Self
155:144°
63:and
50:Type
3244:is
2930:p10
2922:d10
2911:g10
2884:r20
2867:, Z
2863:, Z
2837:Dih
2270:as
2228:cos
2202:cos
2140:2.5
2016:sin
1877:tan
1750:cot
1008:is
765:180
197:In
4248::
3682:.
3603:^
3582:^
3486:^
3459:,
3416:31
3402:11
3352:,
3262:5d
3252:,
3238:A
3223:A
3217:.
3060:,
2917:.
2888:a1
2875:.
2861:10
2839:10
2709:10
2679:10
2635:10
2596:10
2590:DA
2456:AH
2449:GE
2354:.
2240:10
2219:10
2174:,
1892:10
1874:10
1765:10
1697:.
1455:10
1345:.
1094:10
1050:10
991:10
877:36
864:36
851:72
797:36
784:72
756:10
702:72
680:10
658:10
569:10
515:10
379:10
362:.
233:A
178:,
174:,
170:,
166:,
138:10
136:(D
69:10
3737:)
3733:(
3723:e
3716:t
3709:v
3688:.
3577:.
3557:a
3538:.
3511:.
3414:1
3400:4
3376:5
3374:B
3370:6
3368:D
3364:9
3362:A
3354:h
3062:m
3054:m
3052:(
3050:m
3046:m
2904:g
2900:i
2896:p
2892:d
2873:1
2869:2
2865:5
2853:1
2849:2
2845:5
2772:.
2759:=
2754:2
2748:5
2743:+
2740:1
2734:=
2729:a
2726:R
2721:=
2705:E
2699:1
2695:E
2684:F
2675:E
2667:=
2657:F
2652:1
2648:E
2631:E
2625:1
2621:E
2604:.
2598:F
2594:E
2571:.
2558:=
2553:2
2547:5
2542:+
2539:1
2533:=
2523:M
2520:A
2510:H
2507:A
2500:=
2490:H
2487:M
2477:M
2474:A
2451:3
2427:.
2395:.
2310:.
2303:5
2298:2
2295:+
2292:5
2287:a
2284:=
2281:d
2251:,
2247:)
2225:+
2212:3
2198:(
2194:a
2191:2
2188:=
2185:d
2160:d
2146:a
2143:d
2137:=
2134:A
2109:2
2105:R
2091:2
2085:5
2077:5
2068:2
2064:R
2058:2
2055:5
2050:=
2045:2
2041:R
2036:)
2031:5
2023:(
2013:5
2010:=
2007:A
1994:R
1972:2
1968:r
1954:)
1948:5
1943:2
1937:5
1933:(
1929:5
1922:2
1918:r
1914:2
1911:=
1906:2
1902:r
1897:)
1884:(
1871:=
1868:A
1851:r
1829:2
1825:a
1810:5
1805:2
1802:+
1799:5
1792:2
1788:a
1782:2
1779:5
1774:=
1770:)
1757:(
1745:2
1741:a
1735:2
1732:5
1727:=
1724:A
1711:a
1681:5
1676:2
1673:+
1670:5
1663:4
1658:2
1654:a
1648:=
1645:h
1637:2
1634:a
1629:=
1620:A
1594:5
1589:2
1586:+
1583:5
1576:2
1573:a
1568:=
1561:2
1557:)
1553:2
1549:/
1545:a
1542:(
1534:2
1530:R
1524:=
1521:h
1501:]
1498:D
1494:M
1491:[
1470:M
1465:1
1461:E
1451:E
1425:)
1422:1
1419:+
1414:5
1409:(
1404:2
1401:a
1396:=
1390:1
1382:5
1375:a
1372:2
1366:=
1363:R
1324:)
1319:5
1314:+
1311:1
1305:(
1300:2
1297:R
1292:=
1289:a
1267:a
1244:R
1241:a
1233:2
1229:R
1225:=
1220:2
1216:a
1194:0
1188:a
1185:,
1182:R
1158:a
1154:a
1148:R
1142:=
1137:R
1134:a
1104:1
1100:E
1090:E
1086:P
1065:M
1060:1
1056:E
1046:E
1034:.
1022:a
1016:R
996:]
987:E
982:P
979:[
959:a
939:P
918:P
915:M
910:1
906:E
873:=
847:=
844:P
839:1
835:E
831:M
825:m
793:=
777:2
761:=
752:E
746:1
742:E
738:P
732:m
721:.
698:=
693:1
689:E
685:P
676:E
669:m
666:=
663:P
654:E
648:1
644:E
637:m
615:1
611:E
584:P
579:1
575:E
565:E
540:P
520:[
511:E
506:M
503:]
483:a
461:1
457:E
434:a
414:R
394:M
389:1
385:E
375:E
346:R
326:a
300:.
152:)
148:(
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
