267:
254:
40:
202:
polygon because its endpoints must coincide, unlike any
Euclidean line segment. Most definitions of a polygon in Euclidean geometry do not admit the monogon.
1290:
909:
367:
340:
112:
122:
104:
130:
117:
1207:
490:
470:
96:
1097:
465:
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397:
1091:
525:
199:
1219:
1147:
1067:
902:
450:
1153:
475:
360:
88:
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455:
760:
530:
460:
402:
1295:
866:
841:
811:
806:
765:
480:
1264:
1141:
1135:
895:
871:
412:
239:
211:
191:
179:
82:
1254:
1178:
1130:
1103:
1073:
851:
445:
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336:
175:
72:
1259:
1239:
1061:
380:
325:
1213:
1125:
1120:
1085:
1040:
1030:
1020:
1015:
846:
826:
821:
791:
510:
485:
417:
235:
171:
68:
61:
1269:
1172:
1035:
1025:
856:
836:
801:
796:
427:
407:
1284:
1190:
1184:
1079:
1010:
1000:
831:
682:
575:
495:
437:
266:
1005:
861:
731:
687:
651:
641:
636:
215:
143:
49:
1045:
979:
969:
959:
954:
770:
677:
656:
646:
253:
227:
1230:
984:
974:
964:
949:
939:
918:
775:
631:
621:
505:
272:
231:
1244:
750:
740:
717:
707:
697:
626:
535:
500:
243:
944:
755:
745:
702:
661:
590:
580:
570:
389:
259:
223:
155:
1249:
712:
692:
605:
600:
595:
585:
515:
376:
219:
167:
17:
230:
monogonal faces which share one 360° edge and one vertex. Its dual, a
520:
39:
565:
345:
287:
891:
349:
887:
328:, The geometry of geodesics. New York, Academic Press, 1955
1229:
1200:
1165:
1113:
1054:
993:
932:
784:
730:
670:
614:
553:
544:
436:
388:
142:
129:
95:
81:
67:
57:
32:
52:with a single vertex, and one 360-degree arc edge.
214:, a monogon can be constructed as a vertex on a
903:
361:
8:
910:
896:
888:
550:
368:
354:
346:
335:(third edition). Dover Publications Inc.
248:
299:
29:
305:
303:
7:
27:Polygon with one edge and one vertex
927:Listed by number of faces and type
25:
313:, 1969, Second edition, sec 21.3
265:
252:
238:vertices at the poles, one 360°
120:
115:
110:
102:
38:
1291:Polygons by the number of sides
1:
1138:(two infinite groups and 75)
1156:(two infinite groups and 50)
250:
246:) between the two vertices.
1312:
1208:KeplerâPoinsot polyhedron
925:
37:
311:Introduction to geometry
1220:Uniform star polyhedron
1148:quasiregular polyhedron
97:CoxeterâDynkin diagrams
1154:semiregular polyhedron
1201:non-convex polyhedron
206:In spherical geometry
186:In Euclidean geometry
601:Nonagon/Enneagon (9)
531:Tangential trapezoid
242:face, and one edge (
713:Megagon (1,000,000)
481:Isosceles trapezoid
1142:regular polyhedron
1136:uniform polyhedron
1098:Hectotriadiohedron
683:Icositetragon (24)
226:, {1,2}, with two
212:spherical geometry
192:Euclidean geometry
162:, also known as a
1278:
1277:
1179:Archimedean solid
1166:convex polyhedron
1074:Icosidodecahedron
885:
884:
726:
725:
703:Myriagon (10,000)
688:Triacontagon (30)
652:Heptadecagon (17)
642:Pentadecagon (15)
637:Tetradecagon (14)
576:Quadrilateral (4)
446:Antiparallelogram
333:Regular Polytopes
279:
278:
152:
151:
16:(Redirected from
1303:
1114:elemental things
1092:Enneacontahedron
1062:Icositetrahedron
912:
905:
898:
889:
698:Chiliagon (1000)
678:Icositrigon (23)
657:Octadecagon (18)
647:Hexadecagon (16)
551:
370:
363:
356:
347:
331:Coxeter, H.S.M;
326:Herbert Busemann
318:
307:
269:
256:
249:
234:, {2,1} has two
222:). This forms a
125:
124:
123:
119:
118:
114:
113:
107:
106:
105:
42:
30:
21:
1311:
1310:
1306:
1305:
1304:
1302:
1301:
1300:
1281:
1280:
1279:
1274:
1225:
1214:Star polyhedron
1196:
1161:
1109:
1086:Hexecontahedron
1068:Triacontahedron
1050:
1041:Enneadecahedron
1031:Heptadecahedron
1021:Pentadecahedron
1016:Tetradecahedron
989:
928:
921:
916:
886:
881:
780:
734:
722:
666:
632:Tridecagon (13)
622:Hendecagon (11)
610:
546:
540:
511:Right trapezoid
432:
384:
374:
322:
321:
308:
301:
296:
284:
270:
257:
208:
188:
180:Schläfli symbol
138:
121:
116:
111:
109:
103:
101:
83:Schläfli symbol
62:Regular polygon
53:
44:On a circle, a
28:
23:
22:
15:
12:
11:
5:
1309:
1307:
1299:
1298:
1293:
1283:
1282:
1276:
1275:
1273:
1272:
1270:parallelepiped
1267:
1262:
1257:
1252:
1247:
1242:
1236:
1234:
1227:
1226:
1224:
1223:
1217:
1211:
1204:
1202:
1198:
1197:
1195:
1194:
1188:
1182:
1176:
1173:Platonic solid
1169:
1167:
1163:
1162:
1160:
1159:
1158:
1157:
1151:
1145:
1133:
1128:
1123:
1117:
1115:
1111:
1110:
1108:
1107:
1101:
1095:
1089:
1083:
1077:
1071:
1065:
1058:
1056:
1052:
1051:
1049:
1048:
1043:
1038:
1036:Octadecahedron
1033:
1028:
1026:Hexadecahedron
1023:
1018:
1013:
1008:
1003:
997:
995:
991:
990:
988:
987:
982:
977:
972:
967:
962:
957:
952:
947:
942:
936:
934:
930:
929:
926:
923:
922:
917:
915:
914:
907:
900:
892:
883:
882:
880:
879:
874:
869:
864:
859:
854:
849:
844:
839:
837:Pseudotriangle
834:
829:
824:
819:
814:
809:
804:
799:
794:
788:
786:
782:
781:
779:
778:
773:
768:
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758:
753:
748:
743:
737:
735:
728:
727:
724:
723:
721:
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715:
710:
705:
700:
695:
690:
685:
680:
674:
672:
668:
667:
665:
664:
659:
654:
649:
644:
639:
634:
629:
627:Dodecagon (12)
624:
618:
616:
612:
611:
609:
608:
603:
598:
593:
588:
583:
578:
573:
568:
563:
557:
555:
548:
542:
541:
539:
538:
533:
528:
523:
518:
513:
508:
503:
498:
493:
488:
483:
478:
473:
468:
463:
458:
453:
448:
442:
440:
438:Quadrilaterals
434:
433:
431:
430:
425:
420:
415:
410:
405:
400:
394:
392:
386:
385:
375:
373:
372:
365:
358:
350:
344:
343:
329:
320:
319:
298:
297:
295:
292:
291:
290:
283:
280:
277:
276:
263:
207:
204:
187:
184:
150:
149:
146:
140:
139:
136:
133:
131:Symmetry group
127:
126:
99:
93:
92:
85:
79:
78:
75:
65:
64:
59:
55:
54:
43:
35:
34:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1308:
1297:
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1286:
1271:
1268:
1266:
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1248:
1246:
1243:
1241:
1238:
1237:
1235:
1232:
1228:
1221:
1218:
1215:
1212:
1209:
1206:
1205:
1203:
1199:
1192:
1191:Johnson solid
1189:
1186:
1185:Catalan solid
1183:
1180:
1177:
1174:
1171:
1170:
1168:
1164:
1155:
1152:
1149:
1146:
1143:
1140:
1139:
1137:
1134:
1132:
1129:
1127:
1124:
1122:
1119:
1118:
1116:
1112:
1105:
1102:
1099:
1096:
1093:
1090:
1087:
1084:
1081:
1080:Hexoctahedron
1078:
1075:
1072:
1069:
1066:
1063:
1060:
1059:
1057:
1053:
1047:
1044:
1042:
1039:
1037:
1034:
1032:
1029:
1027:
1024:
1022:
1019:
1017:
1014:
1012:
1011:Tridecahedron
1009:
1007:
1004:
1002:
1001:Hendecahedron
999:
998:
996:
992:
986:
983:
981:
978:
976:
973:
971:
968:
966:
963:
961:
958:
956:
953:
951:
948:
946:
943:
941:
938:
937:
935:
931:
924:
920:
913:
908:
906:
901:
899:
894:
893:
890:
878:
877:Weakly simple
875:
873:
870:
868:
865:
863:
860:
858:
855:
853:
850:
848:
845:
843:
840:
838:
835:
833:
830:
828:
825:
823:
820:
818:
817:Infinite skew
815:
813:
810:
808:
805:
803:
800:
798:
795:
793:
790:
789:
787:
783:
777:
774:
772:
769:
767:
764:
762:
759:
757:
754:
752:
749:
747:
744:
742:
739:
738:
736:
733:
732:Star polygons
729:
719:
718:Apeirogon (â)
716:
714:
711:
709:
706:
704:
701:
699:
696:
694:
691:
689:
686:
684:
681:
679:
676:
675:
673:
669:
663:
662:Icosagon (20)
660:
658:
655:
653:
650:
648:
645:
643:
640:
638:
635:
633:
630:
628:
625:
623:
620:
619:
617:
613:
607:
604:
602:
599:
597:
594:
592:
589:
587:
584:
582:
579:
577:
574:
572:
569:
567:
564:
562:
559:
558:
556:
552:
549:
543:
537:
534:
532:
529:
527:
524:
522:
519:
517:
514:
512:
509:
507:
504:
502:
499:
497:
496:Parallelogram
494:
492:
491:Orthodiagonal
489:
487:
484:
482:
479:
477:
474:
472:
471:Ex-tangential
469:
467:
464:
462:
459:
457:
454:
452:
449:
447:
444:
443:
441:
439:
435:
429:
426:
424:
421:
419:
416:
414:
411:
409:
406:
404:
401:
399:
396:
395:
393:
391:
387:
382:
378:
371:
366:
364:
359:
357:
352:
351:
348:
342:
341:0-486-61480-8
338:
334:
330:
327:
324:
323:
316:
312:
306:
304:
300:
293:
289:
286:
285:
281:
274:
268:
264:
261:
255:
251:
247:
245:
241:
237:
233:
229:
228:hemispherical
225:
221:
217:
213:
205:
203:
201:
197:
193:
185:
183:
181:
177:
173:
169:
165:
161:
157:
147:
145:
141:
134:
132:
128:
100:
98:
94:
90:
86:
84:
80:
76:
74:
70:
66:
63:
60:
56:
51:
47:
41:
36:
31:
19:
1104:Apeirohedron
1055:>20 faces
1006:Dodecahedron
671:>20 sides
606:Decagon (10)
591:Heptagon (7)
581:Pentagon (5)
571:Triangle (3)
560:
466:Equidiagonal
332:
317:, p. 386-388
315:Regular maps
314:
310:
216:great circle
209:
195:
189:
163:
159:
153:
144:Dual polygon
50:tessellation
45:
1046:Icosahedron
994:11â20 faces
980:Enneahedron
970:Heptahedron
960:Pentahedron
955:Tetrahedron
867:Star-shaped
842:Rectilinear
812:Equilateral
807:Equiangular
771:Hendecagram
615:11â20 sides
596:Octagon (8)
586:Hexagon (6)
561:Monogon (1)
403:Equilateral
1296:1 (number)
1285:Categories
1231:prismatoid
1216:(infinite)
985:Decahedron
975:Octahedron
965:Hexahedron
940:Monohedron
933:1â10 faces
872:Tangential
776:Dodecagram
554:1â10 sides
545:By number
526:Tangential
506:Right kite
294:References
273:hosohedron
271:Monogonal
258:Monogonal
232:hosohedron
200:degenerate
1245:antiprism
950:Trihedron
919:Polyhedra
852:Reinhardt
761:Enneagram
751:Heptagram
741:Pentagram
708:65537-gon
566:Digon (2)
536:Trapezoid
501:Rectangle
451:Bicentric
413:Isosceles
390:Triangles
309:Coxeter,
236:antipodal
178:. It has
170:with one
148:Self-dual
945:Dihedron
827:Isotoxal
822:Isogonal
766:Decagram
756:Octagram
746:Hexagram
547:of sides
476:Harmonic
377:Polygons
282:See also
275:, {2,1}
262:, {1,2}
260:dihedron
244:meridian
224:dihedron
174:and one
156:geometry
73:vertices
1265:pyramid
1250:frustum
847:Regular
792:Concave
785:Classes
693:257-gon
516:Rhombus
456:Crossed
220:equator
196:monogon
168:polygon
166:, is a
164:henagon
160:monogon
87:{1} or
46:monogon
33:Monogon
18:Henagon
1255:cupola
1131:vertex
857:Simple
802:Cyclic
797:Convex
521:Square
461:Cyclic
423:Obtuse
418:Kepler
339:
176:vertex
1260:wedge
1240:prism
1100:(132)
832:Magic
428:Right
408:Ideal
398:Acute
288:Digon
198:is a
182:{1}.
69:Edges
48:is a
1222:(57)
1193:(92)
1187:(13)
1181:(13)
1150:(16)
1126:edge
1121:face
1094:(90)
1088:(60)
1082:(48)
1076:(32)
1070:(30)
1064:(24)
862:Skew
486:Kite
381:List
337:ISBN
240:lune
172:edge
158:, a
71:and
58:Type
1210:(4)
1175:(5)
1144:(9)
1106:(â)
210:In
190:In
154:In
135:, C
108:or
91:{2}
1287::
1233:âs
302:^
194:a
911:e
904:t
897:v
383:)
379:(
369:e
362:t
355:v
218:(
137:s
89:h
77:1
20:)
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