4867:
4763:
4938:
4980:
4809:
4907:
4992:
4836:
492:
3651:
4824:
3096:
4340:
2721:
2714:
5045:
2870:
2818:
4329:
4450:
4426:
4415:
4391:
3103:
2863:
2811:
4855:
3117:
3028:
442:
3378:
61:
4922:
3035:
2986:
4272:
2240:
2877:
2825:
4461:
4439:
3300:
4380:
3014:
3000:
4693:
3007:
4686:
4250:
4404:
4318:
3627:
5029:
3775:
3110:
3397:
4883:
4672:
3371:
2499:
2490:
2472:
2461:
3089:
4960:
1006:
4261:
4228:
3390:
2220:
2517:
2508:
2481:
4679:
4239:
3786:
2993:
2804:
2086:
4497:
529:
4747:
2203:
2190:
2177:
2162:
2153:
2140:
2129:
2116:
2103:
3284:
3275:
3266:
3255:
3246:
3237:
5014:
4508:
3730:
4369:
3138:
4794:
2596:
2569:
4486:
4779:
3797:
2707:
2856:
4730:
4723:
4716:
4709:
3719:
3131:
3124:
3021:
748:
1219:
1001:{\displaystyle {\begin{aligned}A&={\frac {3{\sqrt {3}}}{2}}R^{2}=3Rr=2{\sqrt {3}}r^{2}\\&={\frac {3{\sqrt {3}}}{8}}D^{2}={\frac {3}{4}}Dd={\frac {\sqrt {3}}{2}}d^{2}\\&\approx 2.598R^{2}\approx 3.464r^{2}\\&\approx 0.6495D^{2}\approx 0.866d^{2}.\end{aligned}}}
1912:
1704:
1539:
696:
4882:
2060:
1087:
4866:
3499:
If, for each side of a cyclic hexagon, the adjacent sides are extended to their intersection, forming a triangle exterior to the given side, then the segments connecting the circumcenters of opposite triangles are
753:
1271:
1710:
4937:
1092:
3934:
4808:
3515:
at the six points (including three triangle vertices) where the extended altitudes of the triangle meet the circumcircle, then the area of the hexagon is twice the area of the triangle.
737:
3874:
350:
3455:
hexagon (one inscribed in a circle) with vertices given by the six intersections of the edges of a triangle and the three lines that are parallel to the edges that pass through its
5239:
1079:
1545:
1380:
3616:
601:
4906:
4762:
1942:
1372:
4921:
4835:
5350:
1345:
1325:
479:
4991:
392:. The longest diagonals of a regular hexagon, connecting diametrically opposite vertices, are twice the length of one side. From this it can be seen that a
1950:
1214:{\displaystyle {\begin{aligned}A&={\frac {ap}{2}}\\&={\frac {r\cdot 4r{\sqrt {3}}}{2}}=2r^{2}{\sqrt {3}}\\&\approx 3.464r^{2}.\end{aligned}}}
4959:
6653:
6083:
3319:
each line is as short as it can possibly be if a large area is to be filled with the fewest hexagons. This means that honeycombs require less
5261:
4746:
5518:
5380:
5314:
5174:
4979:
6113:
5168:
3689:
with equal edge lengths. In three dimensions it will be a zig-zag skew hexagon and can be seen in the vertices and side edges of a
3416:
In addition to the regular hexagon, which determines a unique tessellation of the plane, any irregular hexagon which satisfies the
2669:
2605:
1907:{\displaystyle d_{1}^{4}+d_{3}^{4}+d_{5}^{4}=d_{2}^{4}+d_{4}^{4}+d_{6}^{4}=3\left(\left(R^{2}+L^{2}\right)^{2}+2R^{2}L^{2}\right).}
2679:
2615:
1227:
4823:
4662:
4652:
4642:
4629:
4609:
4586:
4543:
4218:
4208:
4198:
4179:
4169:
4160:
4150:
4140:
4121:
4111:
4092:
4082:
4044:
4034:
4024:
4006:
3996:
2648:
2638:
2588:
2578:
141:
131:
113:
5028:
6648:
4619:
4596:
4576:
4563:
4553:
4454:
4430:
4419:
4395:
4189:
4131:
4102:
4016:
2764:
with evenly many sides, in which case the parallelograms are all rhombi. This decomposition of a regular hexagon is based on a
123:
1280:
If a regular hexagon has successive vertices A, B, C, D, E, F and if P is any point on the circumcircle between B and C, then
2674:
2610:
149:
4854:
4657:
4647:
4624:
4614:
4591:
4581:
4558:
4548:
4213:
4203:
4184:
4174:
4155:
4145:
4126:
4116:
4097:
4087:
4039:
4029:
4011:
4001:
136:
118:
3674:
with six vertices and edges but not existing on the same plane. The interior of such a hexagon is not generally defined. A
2643:
2583:
4635:
3359:
5410:
2338:
hexagon constructed with equal edge lengths, but vertices alternating two different internal angles. These two forms are
5044:
4465:
4443:
3892:
5013:
6236:
6216:
4384:
4276:
3981:
5348:
3439:
until they meet, the three intersection points will lie on a straight line, the "Pascal line" of that configuration.
105:
583:
circle (separation of parallel sides, flat-to-flat distance, short diagonal or height when resting on a flat base),
6658:
6211:
6168:
6143:
5476:
4928:
4913:
4793:
4602:
4408:
2975:
5199:
701:
6271:
5084:
4970:
448:
38:
31:
3839:
429:
are hexagonal for this reason and because the shape makes efficient use of space and building materials. The
324:
6196:
5511:
4254:
3977:
3431:(also known as the "Hexagrammum Mysticum Theorem") states that if an arbitrary hexagon is inscribed in any
441:
6221:
6106:
5067:
4344:
3650:
3528:
2936:
3638:
is constructed externally on each side of any hexagon, then the midpoints of the segments connecting the
1040:
6622:
6562:
6201:
6055:
6048:
6041:
5253:
5233:
5121:
4322:
4265:
4232:
3985:
3965:
3957:
3756:
3324:
2928:
2914:
2656:
2347:
377:
369:
281:
4339:
1699:{\displaystyle d_{1}^{2}+d_{3}^{2}+d_{5}^{2}=d_{2}^{2}+d_{4}^{2}+d_{6}^{2}=3\left(R^{2}+L^{2}\right),}
1534:{\displaystyle d_{1}^{2}+d_{4}^{2}=d_{2}^{2}+d_{5}^{2}=d_{3}^{2}+d_{6}^{2}=2\left(R^{2}+L^{2}\right),}
491:
6506:
6276:
6206:
6148:
5712:
5659:
5127:
5116:
4309:
4299:
4243:
4072:
4062:
3961:
3690:
3655:
3635:
3166:
3076:
2971:
2952:
2940:
2917:
2683:
are also in a hexagonal pattern. The two simple roots of two lengths have a 150° angle between them.
2346:
forms are regular hexagons flattened or stretched along one symmetry direction. It can be seen as an
1274:
506:
457:
423:
397:
314:
284:
45:
5464:
3095:
2869:
2817:
691:{\displaystyle {\frac {1}{2}}d=r=\cos(30^{\circ })R={\frac {\sqrt {3}}{2}}R={\frac {\sqrt {3}}{2}}t}
6643:
6612:
6587:
6557:
6552:
6511:
6226:
6067:
5966:
5716:
5402:
5305:
4950:
4893:
4814:
4778:
4569:
4501:
4449:
4425:
4414:
4390:
4328:
4304:
4285:
4067:
3819:
3428:
3312:
3102:
2862:
2810:
2720:
2224:
1295:
that the height-to-width ratio of a regular hexagon is 1:1.1547005; that is, a hexagon with a long
295:
291:
192:
3568:
3396:
2713:
6617:
6158:
5936:
5886:
5836:
5793:
5763:
5723:
5686:
5504:
5211:
5110:
5005:
3535:
3259:
3203:
2889:
2777:
2311:
1944:
are the distances from the vertices of a regular hexagon to any point on its circumcircle, then
307:
3377:
2903:
277:
95:
4460:
4438:
4271:
3116:
3027:
2876:
2824:
44:"Hexagonal" redirects here. For the FIFA World Cup qualifying tournament in North America, see
6597:
6191:
6099:
6075:
5431:
5257:
5164:
4873:
4845:
4512:
4379:
4373:
4055:
3953:
3686:
3034:
2985:
2956:
404:
299:
154:
85:
60:
5368:
5300:
6126:
6079:
5644:
5633:
5622:
5611:
5602:
5593:
5580:
5558:
5546:
5532:
5528:
5221:
5158:
5094:
5089:
5050:
4897:
4700:
4692:
4536:
3752:
3501:
3417:
3411:
3354:
2907:
2659:
2625:
2465:
2404:
2239:
396:
with a vertex at the center of the regular hexagon and sharing one side with the hexagon is
357:
4685:
4403:
4249:
3013:
2999:
2652:, are in a regular hexagonal pattern. The two simple roots have a 120° angle between them.
2376:
Each subgroup symmetry allows one or more degrees of freedom for irregular forms. Only the
1920:
1350:
6592:
6572:
6567:
6537:
6256:
6231:
6163:
5669:
5654:
5414:
5354:
5079:
5020:
4490:
4317:
3989:
3456:
3448:
3339:
3335:
3006:
2761:
2362:
2335:
2327:
2146:
2122:
430:
271:
200:
196:
81:
74:
3818:
of a hexagon is a diagonal which divides the hexagon into quadrilaterals. In any convex
3774:
3299:
2920:, with Schläfli symbol t{3}. Seen with two types (colors) of edges, this form only has D
6602:
6582:
6547:
6542:
6173:
6153:
6019:
5483:
5098:
4333:
3945:
3790:
3748:
3626:
3512:
3452:
3316:
3185:
3088:
2765:
2663:
2632:
2628:
2498:
2489:
2471:
2460:
1330:
1310:
464:
385:
365:
303:
258:
188:
184:
170:
166:
5264:(Chapter 20, Generalized Schaefli symbols, Types of symmetry of a polygon pp. 275–278)
4260:
4227:
3389:
3109:
2516:
2507:
2480:
6637:
6577:
6428:
6321:
6241:
6183:
6036:
5924:
5917:
5910:
5874:
5867:
5860:
5824:
5817:
5541:
4353:
3436:
3432:
2381:
2243:
The dihedral symmetries are divided depending on whether they pass through vertices (
227:
4678:
4671:
4284:
There are other symmetry polyhedra with stretched or flattened hexagons, like these
4238:
3785:
3370:
2085:
2055:{\displaystyle \left(\sum _{i=1}^{6}d_{i}^{2}\right)^{2}=4\sum _{i=1}^{6}d_{i}^{4}.}
6607:
6477:
6433:
6397:
6387:
6382:
5976:
4496:
3949:
3779:
3671:
3524:
3508:
3331:
3199:
3154:
2836:
2773:
2400:
2370:
2339:
2288:
2219:
2202:
2189:
2176:
2170:
2161:
2152:
2139:
2128:
2115:
2102:
1288:
568:
536:
510:
502:
482:
419:
318:
207:
5408:
2992:
2803:
2740:-gon whose opposite sides are parallel and of equal length) can be dissected into
1327:, whose distances to the centroid of the regular hexagon and its six vertices are
400:, and that the regular hexagon can be partitioned into six equilateral triangles.
3531:
states that the three main diagonals AD, BE, and CF intersect at a single point.
6516:
6423:
6402:
6392:
5985:
5946:
5896:
5846:
5803:
5773:
5705:
5691:
5460:
4997:
4507:
4368:
3969:
3729:
3057:
528:
408:
5454:
3283:
3274:
3265:
3254:
3245:
3236:
6521:
6377:
6367:
6251:
5971:
5955:
5905:
5855:
5812:
5782:
5696:
5470:
4485:
3734:
3708:(same as triangular antiprism) have regular skew hexagons as petrie polygons.
3705:
3180:
3137:
2944:
5434:
2330:
hexagon constructed by three mirrors can alternate long and short edges, and
418:(three hexagons meeting at every vertex), and so are useful for constructing
6496:
6486:
6463:
6453:
6443:
6372:
6281:
6246:
6027:
5941:
5891:
5841:
5798:
5768:
5737:
5480:
5439:
5225:
5075:
5071:
4785:
3973:
3801:
3308:
3068:
2963:
2932:
2595:
2568:
580:
426:
5145:
3486:, then the three main diagonals intersect in a single point if and only if
3315:, hexagonal patterns are prevalent in nature due to their efficiency. In a
2342:
of each other and have half the symmetry order of the regular hexagon. The
1307:
For an arbitrary point in the plane of a regular hexagon with circumradius
433:
of a regular triangular lattice is the honeycomb tessellation of hexagons.
5450:
4729:
4722:
4715:
3796:
2855:
2706:
2275:
symmetry. There are 16 subgroups. There are 8 up to isomorphism: itself (D
2251:
for perpendiculars) Cyclic symmetries in the middle column are labeled as
6501:
6491:
6448:
6407:
6336:
6326:
6316:
6135:
6001:
5756:
5752:
5679:
5487:
5347:
Gutierrez, Antonio, "Hexagon, Inscribed Circle, Tangent, Semiperimeter",
5104:
4966:
4800:
4753:
4476:
3639:
3060:
2948:
1296:
1292:
588:
560:
556:
544:
411:
393:
219:
4708:
3718:
2310:
These symmetries express nine distinct symmetries of a regular hexagon.
2255:
for their central gyration orders. Full symmetry of the regular form is
447:
A step-by-step animation of the construction of a regular hexagon using
6458:
6438:
6351:
6346:
6341:
6306:
6261:
6122:
6010:
5980:
5747:
5742:
5733:
5273:
5063:
5001:
4841:
2733:
2729:
2350:
1299:
of 1.0000000 will have a distance of 0.8660254 between parallel sides.
1016:
1012:
353:
254:
17:
3130:
3123:
6266:
5950:
5900:
5850:
5807:
5777:
5728:
5664:
5301:"Dao's theorem on six circumcenters associated with a cyclic hexagon"
5035:
4889:
2967:
2694:
516:
four times on the circumscribed circle and connect the corner points.
452:
4900:; large masses must cool slowly to form a polygonal fracture pattern
3020:
501:
is given, drawing a circular arc from point A and point B gives the
5216:
6311:
6091:
5369:"Equilateral triangles and Kiepert perspectors in complex numbers"
4769:
3625:
3298:
2955:
by adding a center point. This pattern repeats within the regular
2218:
527:
361:
3334:
and can also tile the plane by translation. In three dimensions,
2369:
hexagons, with opposite sides parallel are also called hexagonal
5700:
5276:, Mathematical recreations and Essays, Thirteenth edition, p.141
3755:, uniform and dual polyhedra and polytopes, shown in these skew
3723:
3701:
3170:
2884:
2769:
6095:
4817:, a hexagonal cloud pattern around the north pole of the planet
3320:
248:
242:
236:
230:
2786:
Dissection of hexagons into three rhombs and parallelograms
1266:{\displaystyle {\tfrac {3{\sqrt {3}}}{2\pi }}\approx 0.8270}
3330:
Irregular hexagons with parallel opposite edges are called
2776:
and projective directions of the cube are dissected within
5124:: abstract board game played on a six-sided hexagonal grid
3630:
Equilateral triangles on the sides of an arbitrary hexagon
3622:
Equilateral triangles on the sides of an arbitrary hexagon
5200:"Cyclic Averages of Regular Polygons and Platonic Solids"
3642:
of opposite triangles form another equilateral triangle.
2403:
can tessellate the
Euclidean plane by translation. Other
2910:, {6,3}, with three hexagonal faces around each vertex.
2069:
595:. The maxima and minima are related by the same factor:
313:
The common length of the sides equals the radius of the
290:
A regular hexagon is defined as a hexagon that is both
3678:
has vertices alternating between two parallel planes.
2690:
2563:
2380:
subgroup has no degrees of freedom but can be seen as
1232:
329:
3895:
3842:
3571:
2361:
can be seen as horizontally and vertically elongated
1953:
1923:
1713:
1548:
1383:
1353:
1333:
1313:
1230:
1090:
1043:
751:
704:
604:
467:
327:
3948:
made of only regular hexagons, because the hexagons
3822:
hexagon (one with all sides equal) with common side
3083:
2980:
2947:
with equilateral triangles on its edges, creating a
2935:, {12}, alternating two types (colors) of edges. An
414:, regular hexagons fit together without any gaps to
6530:
6476:
6416:
6360:
6299:
6290:
6182:
6134:
206:
180:
165:
148:
104:
94:
80:
70:
53:
3929:{\displaystyle {\frac {d_{2}}{a}}>{\sqrt {3}}.}
3928:
3868:
3654:A regular skew hexagon seen as edges (black) of a
3610:
2054:
1936:
1906:
1698:
1533:
1366:
1339:
1319:
1265:
1213:
1073:
1000:
731:
690:
473:
344:
5238:: CS1 maint: DOI inactive as of September 2024 (
3342:and these can tessellate 3-space by translation.
3210:Self-intersecting hexagons with regular vertices
2962:A regular hexagon can be extended into a regular
1015:, the area can also be expressed in terms of the
461:, Book IV, Proposition 15: this is possible as 6
3462:If the successive sides of a cyclic hexagon are
2906:{6}. A regular hexagon is a part of the regular
481:2 × 3, a product of a power of two and distinct
5113:: single path, six-sided star, within a hexagon
2760:parallelograms. In particular this is true for
5204:Communications in Mathematics and Applications
2951:. A regular hexagon can be dissected into six
579:. The minimal diameter or the diameter of the
6107:
5512:
1026:. For the regular hexagon these are given by
287:, t{3}, which alternates two types of edges.
8:
4944:
4931:mirror is composed of 18 hexagonal segments.
3952:, not allowing the result to "fold up". The
2974:around it. This pattern repeats within the
2913:A regular hexagon can also be created as a
6296:
6114:
6100:
6092:
5519:
5505:
5497:
5455:construction with compass and straightedge
4739:Gallery of natural and artificial hexagons
4519:
4472:
4358:
4290:
4050:
3323:to construct and gain much strength under
2782:
2314:labels these by a letter and group order.
732:{\displaystyle d={\frac {\sqrt {3}}{2}}D.}
257:. The total of the internal angles of any
253:, meaning "corner, angle") is a six-sided
5467:a website devoted to hexagon mathematics.
5215:
5163:, Cambridge University Press, p. 9,
5107:: six-sided star within a regular hexagon
3916:
3902:
3896:
3894:
3849:
3843:
3841:
3570:
2043:
2038:
2028:
2017:
2001:
1990:
1985:
1975:
1964:
1952:
1928:
1922:
1890:
1880:
1864:
1853:
1840:
1813:
1808:
1795:
1790:
1777:
1772:
1759:
1754:
1741:
1736:
1723:
1718:
1712:
1682:
1669:
1648:
1643:
1630:
1625:
1612:
1607:
1594:
1589:
1576:
1571:
1558:
1553:
1547:
1517:
1504:
1483:
1478:
1465:
1460:
1447:
1442:
1429:
1424:
1411:
1406:
1393:
1388:
1382:
1358:
1352:
1332:
1312:
1238:
1231:
1229:
1198:
1174:
1168:
1145:
1130:
1105:
1091:
1089:
1064:
1044:
1042:
985:
969:
946:
930:
907:
891:
872:
863:
846:
840:
824:
813:
789:
772:
766:
752:
750:
711:
703:
673:
655:
640:
605:
603:
466:
328:
326:
261:(non-self-intersecting) hexagon is 720°.
5338:, Dover Publications, 2007 (orig. 1960).
5193:
5191:
3869:{\displaystyle {\frac {d_{1}}{a}}\leq 2}
3761:
3710:
3649:
3344:
3338:with parallel opposite faces are called
3208:
2409:
2238:
2078:
6084:List of regular polytopes and compounds
5138:
4742:
1224:The regular hexagon fills the fraction
345:{\displaystyle {\tfrac {2}{\sqrt {3}}}}
5451:Definition and properties of a hexagon
5231:
3523:Let ABCDEF be a hexagon formed by six
50:
5461:An Introduction to Hexagonal Geometry
4876:composed of hexagonal aromatic rings.
4860:Hexagonal order of bubbles in a foam.
3519:Hexagon tangential to a conic section
280:{6} and can also be constructed as a
7:
5070:figure which, like the hexagon, has
4912:An aerial view of Fort Jefferson in
3826:, there exists a principal diagonal
3424:Hexagon inscribed in a conic section
5285:Cartensen, Jens, "About hexagons",
5256:, (2008) The Symmetries of Things,
4752:The ideal crystalline structure of
3984:. These hexagons can be considered
1074:{\displaystyle {}=6R=4r{\sqrt {3}}}
3956:with some hexagonal faces are the
2772:, with 3 of 6 square faces. Other
25:
4953:for its vaguely hexagonal shape.
3507:If a hexagon has vertices on the
2405:hexagon shapes can tile the plane
587:, is twice the minimal radius or
567:, is twice the maximal radius or
306:(has a circumscribed circle) and
5043:
5027:
5012:
4990:
4978:
4958:
4936:
4920:
4905:
4881:
4865:
4853:
4834:
4822:
4807:
4792:
4777:
4761:
4745:
4728:
4721:
4714:
4707:
4691:
4684:
4677:
4670:
4660:
4655:
4650:
4645:
4640:
4627:
4622:
4617:
4612:
4607:
4594:
4589:
4584:
4579:
4574:
4561:
4556:
4551:
4546:
4541:
4506:
4495:
4484:
4459:
4448:
4437:
4424:
4413:
4402:
4389:
4378:
4367:
4338:
4327:
4316:
4270:
4259:
4248:
4237:
4226:
4216:
4211:
4206:
4201:
4196:
4187:
4182:
4177:
4172:
4167:
4158:
4153:
4148:
4143:
4138:
4129:
4124:
4119:
4114:
4109:
4100:
4095:
4090:
4085:
4080:
4042:
4037:
4032:
4027:
4022:
4014:
4009:
4004:
3999:
3994:
3795:
3784:
3773:
3747:The regular skew hexagon is the
3728:
3717:
3395:
3388:
3376:
3369:
3282:
3273:
3264:
3253:
3244:
3235:
3136:
3129:
3122:
3115:
3108:
3101:
3094:
3087:
3033:
3026:
3019:
3012:
3005:
2998:
2991:
2984:
2943:, {3}. A regular hexagon can be
2875:
2868:
2861:
2854:
2823:
2816:
2809:
2802:
2719:
2712:
2705:
2677:
2672:
2667:
2646:
2641:
2636:
2613:
2608:
2603:
2594:
2586:
2581:
2576:
2567:
2515:
2506:
2497:
2488:
2479:
2470:
2459:
2201:
2188:
2175:
2160:
2151:
2138:
2127:
2114:
2101:
2084:
575:, which equals the side length,
490:
440:
374:rotational symmetry of order six
139:
134:
129:
121:
116:
111:
59:
6654:Polygons by the number of sides
5453:with interactive animation and
5383:from the original on 2015-07-05
5317:from the original on 2014-12-05
5252:John H. Conway, Heidi Burgiel,
5177:from the original on 2016-01-02
4455:augmented truncated tetrahedron
4431:metabiaugmented hexagonal prism
4420:parabiaugmented hexagonal prism
4396:gyroelongated triangular cupola
4294:Hexagons in Goldberg polyhedra
3538:and that has consecutive sides
559:(which corresponds to the long
4523:Tilings with regular hexagons
3346:Hexagonal prism tessellations
2227:of a regular hexagon, with Dih
742:The area of a regular hexagon
646:
633:
1:
5198:Meskhishvili, Mamuka (2020).
5157:Wenninger, Magnus J. (1974),
4362:Johnson solids with hexagons
3751:for these higher dimensional
3712:Skew hexagons on 3-fold axes
3360:Hexagonal prismatic honeycomb
3153:A self-intersecting hexagon (
2407:with different orientations.
2073:Example hexagons by symmetry
1287:It follows from the ratio of
5299:Dergiades, Nikolaos (2014).
4466:triangular hebesphenorotunda
4444:triaugmented hexagonal prism
3611:{\displaystyle a+c+e=b+d+f.}
2898:Related polygons and tilings
368:. A regular hexagon has six
249:
237:
30:For the crystal system, see
5336:Advanced Euclidean Geometry
4385:elongated triangular cupola
4277:truncated icosidodecahedron
3982:truncated icosidodecahedron
2259:and no symmetry is labeled
1282:PE + PF = PA + PB + PC + PD
310:(has an inscribed circle).
6675:
6073:
5500:
5472:Hexagons are the Bestagons
5401:Inequalities proposed in "
4929:James Webb Space Telescope
4914:Dry Tortugas National Park
4522:
4482:
4475:
4435:
4400:
4365:
4361:
4293:
4224:
4053:
3810:Convex equilateral hexagon
3771:
3409:
3233:
2882:
2852:
2830:
2800:
2785:
2524:
2184:
2112:
2080:
302:, meaning that it is both
243:
231:
43:
36:
29:
5289:33(2) (2000–2001), 37–40.
4829:Micrograph of a snowflake
4799:The scutes of a turtle's
4699:
4530:
4409:augmented hexagonal prism
4071:
4066:
3879:and a principal diagonal
3764:
3527:of a conic section. Then
3220:
3214:
3052:Hypertruncated triangles
3051:
2976:rhombitrihexagonal tiling
2888:
2883:
2848:
2845:
2842:
2834:
2796:
2790:
2699:
2543:
2444:
2096:
58:
5085:Hexagonal crystal system
4971:hexagonal crystal system
3435:, and pairs of opposite
3406:Tesselations by hexagons
3303:Giant's Causeway closeup
3206:of the regular hexagon:
2247:for diagonal) or edges (
449:compass and straightedge
39:Hexagon (disambiguation)
32:Hexagonal crystal family
5226:10.26713/cma.v11i3.1420
4872:Crystal structure of a
4356:with regular hexagons:
4255:truncated cuboctahedron
3978:truncated cuboctahedron
3940:Polyhedra with hexagons
3697:, symmetry, order 12.
698: and, similarly,
106:Coxeter–Dynkin diagrams
6649:Constructible polygons
5367:Dao Thanh Oai (2015).
5357:, Accessed 2012-04-17.
5228:(inactive 2024-09-12).
5101:of hexagons in a plane
4945:
4345:Chamfered dodecahedron
3930:
3870:
3757:orthogonal projections
3663:
3631:
3612:
3536:tangential to a circle
3304:
3200:self-crossing hexagons
3194:Self-crossing hexagons
2966:by adding alternating
2902:A regular hexagon has
2318:is full symmetry, and
2307:) and the trivial (e)
2264:
2236:
2056:
2033:
1980:
1938:
1908:
1700:
1535:
1374:respectively, we have
1368:
1341:
1321:
1267:
1215:
1075:
1002:
733:
692:
552:
475:
346:
5287:Mathematical Spectrum
5254:Chaim Goodman-Strauss
4969:crystal, one of many
4848:with hexagonal shape.
4323:Chamfered tetrahedron
4266:truncated icosahedron
4233:truncated tetrahedron
3966:truncated icosahedron
3958:truncated tetrahedron
3931:
3871:
3653:
3629:
3613:
3534:In a hexagon that is
3420:will tile the plane.
3302:
2972:equilateral triangles
2953:equilateral triangles
2939:hexagon, h{6}, is an
2657:Exceptional Lie group
2387:Hexagons of symmetry
2242:
2222:
2057:
2013:
1960:
1939:
1937:{\displaystyle d_{i}}
1909:
1701:
1536:
1369:
1367:{\displaystyle d_{i}}
1342:
1322:
1268:
1216:
1076:
1003:
734:
693:
531:
505:M, the center of the
497:When the side length
476:
382:six lines of symmetry
378:reflection symmetries
370:rotational symmetries
347:
241:, meaning "six", and
6347:Nonagon/Enneagon (9)
6277:Tangential trapezoid
5128:Central place theory
5117:Honeycomb conjecture
5019:Władysław Gliński's
4756:is a hexagonal grid.
4244:truncated octahedron
3962:truncated octahedron
3893:
3840:
3691:triangular antiprism
3683:regular skew hexagon
3676:skew zig-zag hexagon
3662:, , (2*3), order 12.
3656:triangular antiprism
3636:equilateral triangle
3569:
3295:Hexagonal structures
3162:Central {6} in {12}
2941:equilateral triangle
2931:hexagon, t{6}, is a
2918:equilateral triangle
2700:12 rhomb dissection
2655:The 12 roots of the
1951:
1921:
1711:
1546:
1381:
1351:
1331:
1311:
1275:circumscribed circle
1228:
1088:
1041:
749:
702:
602:
507:circumscribed circle
465:
325:
315:circumscribed circle
285:equilateral triangle
46:Hexagonal (CONCACAF)
37:For other uses, see
27:Shape with six sides
6459:Megagon (1,000,000)
6227:Isosceles trapezoid
6068:pentagonal polytope
5967:Uniform 10-polytope
5527:Fundamental convex
5403:Crux Mathematicorum
5373:Forum Geometricorum
5334:Johnson, Roger A.,
5306:Forum Geometricorum
4951:Metropolitan France
4502:Hexagonal antiprism
4286:Goldberg polyhedron
3713:
3529:Brianchon's theorem
3347:
3211:
2778:rectangular cuboids
2662:, represented by a
2631:, represented by a
2624:The 6 roots of the
2235:symmetry, order 12.
2048:
1995:
1818:
1800:
1782:
1764:
1746:
1728:
1653:
1635:
1617:
1599:
1581:
1563:
1488:
1470:
1452:
1434:
1416:
1398:
6429:Icositetragon (24)
5937:Uniform 9-polytope
5887:Uniform 8-polytope
5837:Uniform 7-polytope
5794:Uniform 6-polytope
5764:Uniform 5-polytope
5724:Uniform polychoron
5687:Uniform polyhedron
5535:in dimensions 2–10
5486:about hexagons by
5432:Weisstein, Eric W.
5413:2017-08-30 at the
5353:2012-05-11 at the
5111:Unicursal hexagram
5006:Reading, Berkshire
4056:Archimedean solids
3954:Archimedean solids
3926:
3866:
3816:principal diagonal
3711:
3664:
3632:
3608:
3437:sides are extended
3345:
3305:
3209:
3204:vertex arrangement
3150:A concave hexagon
2890:Rectangular cuboid
2849:Rectangular faces
2732:states that every
2265:
2237:
2052:
2034:
1981:
1934:
1904:
1804:
1786:
1768:
1750:
1732:
1714:
1696:
1639:
1621:
1603:
1585:
1567:
1549:
1531:
1474:
1456:
1438:
1420:
1402:
1384:
1364:
1337:
1317:
1263:
1255:
1211:
1209:
1071:
1022:and the perimeter
998:
996:
729:
688:
553:
471:
342:
340:
6659:Elementary shapes
6631:
6630:
6472:
6471:
6449:Myriagon (10,000)
6434:Triacontagon (30)
6398:Heptadecagon (17)
6388:Pentadecagon (15)
6383:Tetradecagon (14)
6322:Quadrilateral (4)
6192:Antiparallelogram
6089:
6088:
6076:Polytope families
5533:uniform polytopes
5262:978-1-56881-220-5
5160:Polyhedron Models
5038:Botanical Gardens
4888:Naturally formed
4874:molecular hexagon
4846:aromatic compound
4736:
4735:
4701:2-uniform tilings
4518:
4517:
4513:Hexagonal pyramid
4471:
4470:
4374:triangular cupola
4352:There are also 9
4350:
4349:
4282:
4281:
3921:
3911:
3858:
3807:
3806:
3740:
3739:
3687:vertex-transitive
3403:
3402:
3292:
3291:
3191:
3190:
3082:
3081:
2957:triangular tiling
2895:
2894:
2727:
2726:
2622:
2621:
2557:
2556:
2279:), 2 dihedral: (D
2223:The six lines of
2217:
2216:
2213:
2212:
1340:{\displaystyle L}
1320:{\displaystyle R}
1254:
1243:
1179:
1156:
1150:
1118:
1069:
901:
897:
880:
857:
851:
818:
783:
777:
721:
717:
683:
679:
665:
661:
613:
563:of the hexagon),
474:{\displaystyle =}
422:. The cells of a
384:), making up the
339:
338:
216:
215:
65:A regular hexagon
16:(Redirected from
6666:
6444:Chiliagon (1000)
6424:Icositrigon (23)
6403:Octadecagon (18)
6393:Hexadecagon (16)
6297:
6116:
6109:
6102:
6093:
6080:Regular polytope
5641:
5630:
5619:
5578:
5521:
5514:
5507:
5498:
5473:
5445:
5444:
5418:
5398:
5392:
5391:
5389:
5388:
5364:
5358:
5345:
5339:
5332:
5326:
5325:
5323:
5322:
5296:
5290:
5283:
5277:
5271:
5265:
5250:
5244:
5243:
5237:
5229:
5219:
5195:
5186:
5184:
5183:
5182:
5154:
5148:
5143:
5095:Hexagonal tiling
5090:Hexagonal number
5078:and tessellates
5068:four-dimensional
5051:Hexagonal window
5047:
5034:Pavilion in the
5031:
5016:
4994:
4982:
4962:
4948:
4940:
4924:
4909:
4898:Northern Ireland
4894:Giant's Causeway
4885:
4869:
4857:
4838:
4826:
4815:Saturn's hexagon
4811:
4796:
4781:
4765:
4749:
4732:
4725:
4718:
4711:
4695:
4688:
4681:
4674:
4665:
4664:
4663:
4659:
4658:
4654:
4653:
4649:
4648:
4644:
4643:
4632:
4631:
4630:
4626:
4625:
4621:
4620:
4616:
4615:
4611:
4610:
4599:
4598:
4597:
4593:
4592:
4588:
4587:
4583:
4582:
4578:
4577:
4566:
4565:
4564:
4560:
4559:
4555:
4554:
4550:
4549:
4545:
4544:
4520:
4510:
4499:
4488:
4473:
4463:
4452:
4441:
4428:
4417:
4406:
4393:
4382:
4371:
4359:
4342:
4331:
4320:
4291:
4274:
4263:
4252:
4241:
4230:
4221:
4220:
4219:
4215:
4214:
4210:
4209:
4205:
4204:
4200:
4199:
4192:
4191:
4190:
4186:
4185:
4181:
4180:
4176:
4175:
4171:
4170:
4163:
4162:
4161:
4157:
4156:
4152:
4151:
4147:
4146:
4142:
4141:
4134:
4133:
4132:
4128:
4127:
4123:
4122:
4118:
4117:
4113:
4112:
4105:
4104:
4103:
4099:
4098:
4094:
4093:
4089:
4088:
4084:
4083:
4051:
4047:
4046:
4045:
4041:
4040:
4036:
4035:
4031:
4030:
4026:
4025:
4019:
4018:
4017:
4013:
4012:
4008:
4007:
4003:
4002:
3998:
3997:
3990:Coxeter diagrams
3988:triangles, with
3935:
3933:
3932:
3927:
3922:
3917:
3912:
3907:
3906:
3897:
3875:
3873:
3872:
3867:
3859:
3854:
3853:
3844:
3799:
3788:
3777:
3762:
3732:
3721:
3714:
3617:
3615:
3614:
3609:
3495:
3429:Pascal's theorem
3418:Conway criterion
3412:Hexagonal tiling
3399:
3392:
3380:
3373:
3355:Hexagonal tiling
3348:
3340:parallelohedrons
3336:hexagonal prisms
3313:Giant's Causeway
3286:
3277:
3268:
3257:
3248:
3239:
3212:
3140:
3133:
3126:
3119:
3112:
3105:
3098:
3091:
3084:
3037:
3030:
3023:
3016:
3009:
3002:
2995:
2988:
2981:
2908:hexagonal tiling
2879:
2872:
2865:
2858:
2827:
2820:
2813:
2806:
2783:
2768:projection of a
2762:regular polygons
2759:
2750:
2749:
2745:
2723:
2716:
2709:
2691:
2682:
2681:
2680:
2676:
2675:
2671:
2670:
2651:
2650:
2649:
2645:
2644:
2640:
2639:
2626:simple Lie group
2618:
2617:
2616:
2612:
2611:
2607:
2606:
2598:
2591:
2590:
2589:
2585:
2584:
2580:
2579:
2571:
2564:
2560:A2 and G2 groups
2519:
2510:
2501:
2492:
2483:
2474:
2463:
2410:
2322:is no symmetry.
2205:
2192:
2179:
2164:
2155:
2142:
2131:
2118:
2105:
2088:
2079:
2070:
2061:
2059:
2058:
2053:
2047:
2042:
2032:
2027:
2006:
2005:
2000:
1996:
1994:
1989:
1979:
1974:
1943:
1941:
1940:
1935:
1933:
1932:
1913:
1911:
1910:
1905:
1900:
1896:
1895:
1894:
1885:
1884:
1869:
1868:
1863:
1859:
1858:
1857:
1845:
1844:
1817:
1812:
1799:
1794:
1781:
1776:
1763:
1758:
1745:
1740:
1727:
1722:
1705:
1703:
1702:
1697:
1692:
1688:
1687:
1686:
1674:
1673:
1652:
1647:
1634:
1629:
1616:
1611:
1598:
1593:
1580:
1575:
1562:
1557:
1540:
1538:
1537:
1532:
1527:
1523:
1522:
1521:
1509:
1508:
1487:
1482:
1469:
1464:
1451:
1446:
1433:
1428:
1415:
1410:
1397:
1392:
1373:
1371:
1370:
1365:
1363:
1362:
1346:
1344:
1343:
1338:
1326:
1324:
1323:
1318:
1283:
1272:
1270:
1269:
1264:
1256:
1253:
1245:
1244:
1239:
1233:
1220:
1218:
1217:
1212:
1210:
1203:
1202:
1184:
1180:
1175:
1173:
1172:
1157:
1152:
1151:
1146:
1131:
1123:
1119:
1114:
1106:
1080:
1078:
1077:
1072:
1070:
1065:
1045:
1011:For any regular
1007:
1005:
1004:
999:
997:
990:
989:
974:
973:
955:
951:
950:
935:
934:
916:
912:
911:
902:
893:
892:
881:
873:
868:
867:
858:
853:
852:
847:
841:
833:
829:
828:
819:
814:
794:
793:
784:
779:
778:
773:
767:
738:
736:
735:
730:
722:
713:
712:
697:
695:
694:
689:
684:
675:
674:
666:
657:
656:
645:
644:
614:
606:
515:
500:
494:
480:
478:
477:
472:
444:
360:). All internal
358:inscribed circle
351:
349:
348:
343:
341:
334:
330:
252:
246:
245:
240:
234:
233:
144:
143:
142:
138:
137:
133:
132:
126:
125:
124:
120:
119:
115:
114:
63:
51:
21:
6674:
6673:
6669:
6668:
6667:
6665:
6664:
6663:
6634:
6633:
6632:
6627:
6526:
6480:
6468:
6412:
6378:Tridecagon (13)
6368:Hendecagon (11)
6356:
6292:
6286:
6257:Right trapezoid
6178:
6130:
6120:
6090:
6059:
6052:
6045:
5928:
5921:
5914:
5878:
5871:
5864:
5828:
5821:
5655:Regular polygon
5648:
5639:
5632:
5628:
5621:
5617:
5608:
5599:
5592:
5588:
5576:
5570:
5566:
5554:
5536:
5525:
5494:
5471:
5430:
5429:
5426:
5421:
5415:Wayback Machine
5399:
5395:
5386:
5384:
5366:
5365:
5361:
5355:Wayback Machine
5346:
5342:
5333:
5329:
5320:
5318:
5298:
5297:
5293:
5284:
5280:
5272:
5268:
5251:
5247:
5230:
5197:
5196:
5189:
5180:
5178:
5171:
5156:
5155:
5151:
5144:
5140:
5136:
5080:Euclidean space
5060:
5053:
5048:
5039:
5032:
5023:
5021:hexagonal chess
5017:
5008:
4995:
4986:
4983:
4974:
4963:
4954:
4941:
4932:
4925:
4916:
4910:
4901:
4886:
4877:
4870:
4861:
4858:
4849:
4844:, the simplest
4839:
4830:
4827:
4818:
4812:
4803:
4797:
4788:
4782:
4773:
4772:mirror segments
4766:
4757:
4750:
4741:
4661:
4656:
4651:
4646:
4641:
4639:
4638:
4628:
4623:
4618:
4613:
4608:
4606:
4605:
4595:
4590:
4585:
4580:
4575:
4573:
4572:
4562:
4557:
4552:
4547:
4542:
4540:
4539:
4511:
4500:
4491:Hexagonal prism
4489:
4464:
4453:
4442:
4429:
4418:
4407:
4394:
4383:
4372:
4343:
4332:
4321:
4275:
4264:
4253:
4242:
4231:
4217:
4212:
4207:
4202:
4197:
4195:
4188:
4183:
4178:
4173:
4168:
4166:
4159:
4154:
4149:
4144:
4139:
4137:
4130:
4125:
4120:
4115:
4110:
4108:
4101:
4096:
4091:
4086:
4081:
4079:
4043:
4038:
4033:
4028:
4023:
4021:
4015:
4010:
4005:
4000:
3995:
3993:
3942:
3898:
3891:
3890:
3885:
3845:
3838:
3837:
3832:
3812:
3800:
3789:
3778:
3745:
3743:Petrie polygons
3733:
3722:
3696:
3693:with the same D
3661:
3648:
3624:
3567:
3566:
3521:
3487:
3457:symmedian point
3449:Lemoine hexagon
3445:
3426:
3414:
3408:
3385:Parallelogonal
3297:
3287:
3278:
3269:
3258:
3249:
3240:
3230:
3224:
3218:
3196:
3179:
3161:
3146:
3074:
3066:
3056:
3048:
3043:
2923:
2904:Schläfli symbol
2900:
2797:Parallelograms
2747:
2743:
2742:
2741:
2689:
2678:
2673:
2668:
2666:
2647:
2642:
2637:
2635:
2614:
2609:
2604:
2602:
2601:
2599:
2587:
2582:
2577:
2575:
2574:
2572:
2562:
2553:
2547:
2541:
2535:
2529:
2520:
2511:
2502:
2493:
2484:
2475:
2464:
2306:
2302:
2298:
2294:
2286:
2282:
2278:
2274:
2269:regular hexagon
2230:
2206:
2193:
2180:
2169:
2167:
2165:
2156:
2145:
2143:
2134:
2132:
2121:
2119:
2106:
2091:
2089:
2068:
1959:
1955:
1954:
1949:
1948:
1924:
1919:
1918:
1886:
1876:
1849:
1836:
1835:
1831:
1830:
1829:
1825:
1709:
1708:
1678:
1665:
1664:
1660:
1544:
1543:
1513:
1500:
1499:
1495:
1379:
1378:
1354:
1349:
1348:
1329:
1328:
1309:
1308:
1305:
1281:
1246:
1234:
1226:
1225:
1208:
1207:
1194:
1182:
1181:
1164:
1132:
1121:
1120:
1107:
1098:
1086:
1085:
1039:
1038:
995:
994:
981:
965:
953:
952:
942:
926:
914:
913:
903:
859:
842:
831:
830:
820:
785:
768:
759:
747:
746:
700:
699:
636:
600:
599:
526:
521:
520:
519:
518:
517:
513:
509:. Transfer the
498:
495:
487:
486:
463:
462:
445:
431:Voronoi diagram
391:
356:(radius of the
323:
322:
321:, which equals
278:Schläfli symbol
267:
265:Regular hexagon
160:
140:
135:
130:
128:
127:
122:
117:
112:
110:
96:Schläfli symbol
75:Regular polygon
66:
54:Regular hexagon
49:
42:
35:
28:
23:
22:
15:
12:
11:
5:
6672:
6670:
6662:
6661:
6656:
6651:
6646:
6636:
6635:
6629:
6628:
6626:
6625:
6620:
6615:
6610:
6605:
6600:
6595:
6590:
6585:
6583:Pseudotriangle
6580:
6575:
6570:
6565:
6560:
6555:
6550:
6545:
6540:
6534:
6532:
6528:
6527:
6525:
6524:
6519:
6514:
6509:
6504:
6499:
6494:
6489:
6483:
6481:
6474:
6473:
6470:
6469:
6467:
6466:
6461:
6456:
6451:
6446:
6441:
6436:
6431:
6426:
6420:
6418:
6414:
6413:
6411:
6410:
6405:
6400:
6395:
6390:
6385:
6380:
6375:
6373:Dodecagon (12)
6370:
6364:
6362:
6358:
6357:
6355:
6354:
6349:
6344:
6339:
6334:
6329:
6324:
6319:
6314:
6309:
6303:
6301:
6294:
6288:
6287:
6285:
6284:
6279:
6274:
6269:
6264:
6259:
6254:
6249:
6244:
6239:
6234:
6229:
6224:
6219:
6214:
6209:
6204:
6199:
6194:
6188:
6186:
6184:Quadrilaterals
6180:
6179:
6177:
6176:
6171:
6166:
6161:
6156:
6151:
6146:
6140:
6138:
6132:
6131:
6121:
6119:
6118:
6111:
6104:
6096:
6087:
6086:
6071:
6070:
6061:
6057:
6050:
6043:
6039:
6030:
6013:
6004:
5993:
5992:
5990:
5988:
5983:
5974:
5969:
5963:
5962:
5960:
5958:
5953:
5944:
5939:
5933:
5932:
5930:
5926:
5919:
5912:
5908:
5903:
5894:
5889:
5883:
5882:
5880:
5876:
5869:
5862:
5858:
5853:
5844:
5839:
5833:
5832:
5830:
5826:
5819:
5815:
5810:
5801:
5796:
5790:
5789:
5787:
5785:
5780:
5771:
5766:
5760:
5759:
5750:
5745:
5740:
5731:
5726:
5720:
5719:
5710:
5708:
5703:
5694:
5689:
5683:
5682:
5677:
5672:
5667:
5662:
5657:
5651:
5650:
5646:
5642:
5637:
5626:
5615:
5606:
5597:
5590:
5584:
5574:
5568:
5562:
5556:
5550:
5544:
5538:
5537:
5526:
5524:
5523:
5516:
5509:
5501:
5496:
5492:
5491:
5484:internet video
5468:
5458:
5447:
5446:
5425:
5424:External links
5422:
5420:
5419:
5393:
5359:
5340:
5327:
5291:
5278:
5266:
5245:
5187:
5169:
5149:
5137:
5135:
5132:
5131:
5130:
5125:
5119:
5114:
5108:
5102:
5099:regular tiling
5092:
5087:
5082:
5059:
5056:
5055:
5054:
5049:
5042:
5040:
5033:
5026:
5024:
5018:
5011:
5009:
5000:, a hexagonal
4996:
4989:
4987:
4985:Hexagonal barn
4984:
4977:
4975:
4964:
4957:
4955:
4942:
4935:
4933:
4926:
4919:
4917:
4911:
4904:
4902:
4887:
4880:
4878:
4871:
4864:
4862:
4859:
4852:
4850:
4840:
4833:
4831:
4828:
4821:
4819:
4813:
4806:
4804:
4798:
4791:
4789:
4783:
4776:
4774:
4767:
4760:
4758:
4751:
4744:
4740:
4737:
4734:
4733:
4726:
4719:
4712:
4704:
4703:
4697:
4696:
4689:
4682:
4675:
4667:
4666:
4633:
4600:
4567:
4533:
4532:
4529:
4525:
4524:
4516:
4515:
4504:
4493:
4481:
4480:
4479:with hexagons
4469:
4468:
4457:
4446:
4434:
4433:
4422:
4411:
4399:
4398:
4387:
4376:
4364:
4363:
4354:Johnson solids
4348:
4347:
4336:
4334:Chamfered cube
4325:
4313:
4312:
4307:
4302:
4296:
4295:
4280:
4279:
4268:
4257:
4246:
4235:
4223:
4222:
4193:
4164:
4135:
4106:
4076:
4075:
4070:
4065:
4059:
4058:
3946:Platonic solid
3941:
3938:
3937:
3936:
3925:
3920:
3915:
3910:
3905:
3901:
3883:
3877:
3876:
3865:
3862:
3857:
3852:
3848:
3830:
3811:
3808:
3805:
3804:
3793:
3791:3-3 duopyramid
3782:
3770:
3769:
3766:
3749:Petrie polygon
3744:
3741:
3738:
3737:
3726:
3694:
3659:
3647:
3644:
3623:
3620:
3619:
3618:
3607:
3604:
3601:
3598:
3595:
3592:
3589:
3586:
3583:
3580:
3577:
3574:
3520:
3517:
3513:acute triangle
3444:
3443:Cyclic hexagon
3441:
3425:
3422:
3410:Main article:
3407:
3404:
3401:
3400:
3393:
3386:
3382:
3381:
3374:
3367:
3363:
3362:
3357:
3352:
3317:hexagonal grid
3296:
3293:
3290:
3289:
3280:
3271:
3262:
3251:
3242:
3232:
3231:
3228:
3225:
3222:
3219:
3216:
3198:There are six
3195:
3192:
3189:
3188:
3186:Complete graph
3183:
3176:
3175:Dissected {6}
3173:
3163:
3158:
3151:
3148:
3142:
3141:
3134:
3127:
3120:
3113:
3106:
3099:
3092:
3080:
3079:
3071:
3063:
3053:
3050:
3045:
3039:
3038:
3031:
3024:
3017:
3010:
3003:
2996:
2989:
2921:
2899:
2896:
2893:
2892:
2887:
2881:
2880:
2873:
2866:
2859:
2851:
2850:
2847:
2844:
2840:
2839:
2833:
2829:
2828:
2821:
2814:
2807:
2799:
2798:
2795:
2792:
2788:
2787:
2766:Petrie polygon
2725:
2724:
2717:
2710:
2702:
2701:
2698:
2688:
2685:
2664:Dynkin diagram
2633:Dynkin diagram
2620:
2619:
2600:G2 group roots
2592:
2573:A2 group roots
2561:
2558:
2555:
2554:
2551:
2548:
2545:
2542:
2539:
2536:
2533:
2530:
2527:
2523:
2522:
2513:
2504:
2495:
2486:
2477:
2468:
2456:
2455:
2449:
2443:
2433:
2427:
2421:
2382:directed edges
2304:
2300:
2296:
2292:
2284:
2280:
2276:
2272:
2228:
2215:
2214:
2211:
2210:
2208:
2199:
2197:
2195:
2186:
2183:
2182:
2173:
2158:
2149:
2136:
2125:
2111:
2110:
2108:
2099:
2097:
2095:
2093:
2082:
2075:
2074:
2067:
2064:
2063:
2062:
2051:
2046:
2041:
2037:
2031:
2026:
2023:
2020:
2016:
2012:
2009:
2004:
1999:
1993:
1988:
1984:
1978:
1973:
1970:
1967:
1963:
1958:
1931:
1927:
1915:
1914:
1903:
1899:
1893:
1889:
1883:
1879:
1875:
1872:
1867:
1862:
1856:
1852:
1848:
1843:
1839:
1834:
1828:
1824:
1821:
1816:
1811:
1807:
1803:
1798:
1793:
1789:
1785:
1780:
1775:
1771:
1767:
1762:
1757:
1753:
1749:
1744:
1739:
1735:
1731:
1726:
1721:
1717:
1706:
1695:
1691:
1685:
1681:
1677:
1672:
1668:
1663:
1659:
1656:
1651:
1646:
1642:
1638:
1633:
1628:
1624:
1620:
1615:
1610:
1606:
1602:
1597:
1592:
1588:
1584:
1579:
1574:
1570:
1566:
1561:
1556:
1552:
1541:
1530:
1526:
1520:
1516:
1512:
1507:
1503:
1498:
1494:
1491:
1486:
1481:
1477:
1473:
1468:
1463:
1459:
1455:
1450:
1445:
1441:
1437:
1432:
1427:
1423:
1419:
1414:
1409:
1405:
1401:
1396:
1391:
1387:
1361:
1357:
1336:
1316:
1304:
1303:Point in plane
1301:
1262:
1259:
1252:
1249:
1242:
1237:
1222:
1221:
1206:
1201:
1197:
1193:
1190:
1187:
1185:
1183:
1178:
1171:
1167:
1163:
1160:
1155:
1149:
1144:
1141:
1138:
1135:
1129:
1126:
1124:
1122:
1117:
1113:
1110:
1104:
1101:
1099:
1097:
1094:
1093:
1068:
1063:
1060:
1057:
1054:
1051:
1048:
1009:
1008:
993:
988:
984:
980:
977:
972:
968:
964:
961:
958:
956:
954:
949:
945:
941:
938:
933:
929:
925:
922:
919:
917:
915:
910:
906:
900:
896:
890:
887:
884:
879:
876:
871:
866:
862:
856:
850:
845:
839:
836:
834:
832:
827:
823:
817:
812:
809:
806:
803:
800:
797:
792:
788:
782:
776:
771:
765:
762:
760:
758:
755:
754:
740:
739:
728:
725:
720:
716:
710:
707:
687:
682:
678:
672:
669:
664:
660:
654:
651:
648:
643:
639:
635:
632:
629:
626:
623:
620:
617:
612:
609:
525:
522:
496:
489:
488:
470:
446:
439:
438:
437:
436:
435:
416:tile the plane
389:
386:dihedral group
337:
333:
266:
263:
214:
213:
210:
204:
203:
182:
178:
177:
174:
167:Internal angle
163:
162:
158:
152:
150:Symmetry group
146:
145:
108:
102:
101:
98:
92:
91:
88:
78:
77:
72:
68:
67:
64:
56:
55:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6671:
6660:
6657:
6655:
6652:
6650:
6647:
6645:
6642:
6641:
6639:
6624:
6623:Weakly simple
6621:
6619:
6616:
6614:
6611:
6609:
6606:
6604:
6601:
6599:
6596:
6594:
6591:
6589:
6586:
6584:
6581:
6579:
6576:
6574:
6571:
6569:
6566:
6564:
6563:Infinite skew
6561:
6559:
6556:
6554:
6551:
6549:
6546:
6544:
6541:
6539:
6536:
6535:
6533:
6529:
6523:
6520:
6518:
6515:
6513:
6510:
6508:
6505:
6503:
6500:
6498:
6495:
6493:
6490:
6488:
6485:
6484:
6482:
6479:
6478:Star polygons
6475:
6465:
6464:Apeirogon (∞)
6462:
6460:
6457:
6455:
6452:
6450:
6447:
6445:
6442:
6440:
6437:
6435:
6432:
6430:
6427:
6425:
6422:
6421:
6419:
6415:
6409:
6408:Icosagon (20)
6406:
6404:
6401:
6399:
6396:
6394:
6391:
6389:
6386:
6384:
6381:
6379:
6376:
6374:
6371:
6369:
6366:
6365:
6363:
6359:
6353:
6350:
6348:
6345:
6343:
6340:
6338:
6335:
6333:
6330:
6328:
6325:
6323:
6320:
6318:
6315:
6313:
6310:
6308:
6305:
6304:
6302:
6298:
6295:
6289:
6283:
6280:
6278:
6275:
6273:
6270:
6268:
6265:
6263:
6260:
6258:
6255:
6253:
6250:
6248:
6245:
6243:
6242:Parallelogram
6240:
6238:
6237:Orthodiagonal
6235:
6233:
6230:
6228:
6225:
6223:
6220:
6218:
6217:Ex-tangential
6215:
6213:
6210:
6208:
6205:
6203:
6200:
6198:
6195:
6193:
6190:
6189:
6187:
6185:
6181:
6175:
6172:
6170:
6167:
6165:
6162:
6160:
6157:
6155:
6152:
6150:
6147:
6145:
6142:
6141:
6139:
6137:
6133:
6128:
6124:
6117:
6112:
6110:
6105:
6103:
6098:
6097:
6094:
6085:
6081:
6077:
6072:
6069:
6065:
6062:
6060:
6053:
6046:
6040:
6038:
6034:
6031:
6029:
6025:
6021:
6017:
6014:
6012:
6008:
6005:
6003:
5999:
5995:
5994:
5991:
5989:
5987:
5984:
5982:
5978:
5975:
5973:
5970:
5968:
5965:
5964:
5961:
5959:
5957:
5954:
5952:
5948:
5945:
5943:
5940:
5938:
5935:
5934:
5931:
5929:
5922:
5915:
5909:
5907:
5904:
5902:
5898:
5895:
5893:
5890:
5888:
5885:
5884:
5881:
5879:
5872:
5865:
5859:
5857:
5854:
5852:
5848:
5845:
5843:
5840:
5838:
5835:
5834:
5831:
5829:
5822:
5816:
5814:
5811:
5809:
5805:
5802:
5800:
5797:
5795:
5792:
5791:
5788:
5786:
5784:
5781:
5779:
5775:
5772:
5770:
5767:
5765:
5762:
5761:
5758:
5754:
5751:
5749:
5746:
5744:
5743:Demitesseract
5741:
5739:
5735:
5732:
5730:
5727:
5725:
5722:
5721:
5718:
5714:
5711:
5709:
5707:
5704:
5702:
5698:
5695:
5693:
5690:
5688:
5685:
5684:
5681:
5678:
5676:
5673:
5671:
5668:
5666:
5663:
5661:
5658:
5656:
5653:
5652:
5649:
5643:
5640:
5636:
5629:
5625:
5618:
5614:
5609:
5605:
5600:
5596:
5591:
5589:
5587:
5583:
5573:
5569:
5567:
5565:
5561:
5557:
5555:
5553:
5549:
5545:
5543:
5540:
5539:
5534:
5530:
5522:
5517:
5515:
5510:
5508:
5503:
5502:
5499:
5495:
5489:
5485:
5482:
5478:
5474:
5469:
5466:
5462:
5459:
5456:
5452:
5449:
5448:
5442:
5441:
5436:
5433:
5428:
5427:
5423:
5416:
5412:
5409:
5406:
5404:
5397:
5394:
5382:
5378:
5374:
5370:
5363:
5360:
5356:
5352:
5349:
5344:
5341:
5337:
5331:
5328:
5316:
5312:
5308:
5307:
5302:
5295:
5292:
5288:
5282:
5279:
5275:
5270:
5267:
5263:
5259:
5255:
5249:
5246:
5241:
5235:
5227:
5223:
5218:
5213:
5209:
5205:
5201:
5194:
5192:
5188:
5176:
5172:
5170:9780521098595
5166:
5162:
5161:
5153:
5150:
5147:
5142:
5139:
5133:
5129:
5126:
5123:
5120:
5118:
5115:
5112:
5109:
5106:
5103:
5100:
5096:
5093:
5091:
5088:
5086:
5083:
5081:
5077:
5073:
5069:
5065:
5062:
5061:
5057:
5052:
5046:
5041:
5037:
5030:
5025:
5022:
5015:
5010:
5007:
5003:
4999:
4993:
4988:
4981:
4976:
4972:
4968:
4961:
4956:
4952:
4947:
4939:
4934:
4930:
4923:
4918:
4915:
4908:
4903:
4899:
4895:
4892:columns from
4891:
4884:
4879:
4875:
4868:
4863:
4856:
4851:
4847:
4843:
4837:
4832:
4825:
4820:
4816:
4810:
4805:
4802:
4795:
4790:
4787:
4780:
4775:
4771:
4764:
4759:
4755:
4748:
4743:
4738:
4731:
4727:
4724:
4720:
4717:
4713:
4710:
4706:
4705:
4702:
4698:
4694:
4690:
4687:
4683:
4680:
4676:
4673:
4669:
4668:
4637:
4634:
4604:
4601:
4571:
4568:
4538:
4535:
4534:
4527:
4526:
4521:
4514:
4509:
4505:
4503:
4498:
4494:
4492:
4487:
4483:
4478:
4474:
4467:
4462:
4458:
4456:
4451:
4447:
4445:
4440:
4436:
4432:
4427:
4423:
4421:
4416:
4412:
4410:
4405:
4401:
4397:
4392:
4388:
4386:
4381:
4377:
4375:
4370:
4366:
4360:
4357:
4355:
4346:
4341:
4337:
4335:
4330:
4326:
4324:
4319:
4315:
4314:
4311:
4308:
4306:
4303:
4301:
4298:
4297:
4292:
4289:
4287:
4278:
4273:
4269:
4267:
4262:
4258:
4256:
4251:
4247:
4245:
4240:
4236:
4234:
4229:
4225:
4194:
4165:
4136:
4107:
4078:
4077:
4074:
4069:
4064:
4061:
4060:
4057:
4052:
4049:
3991:
3987:
3983:
3979:
3975:
3971:
3967:
3963:
3959:
3955:
3951:
3947:
3939:
3923:
3918:
3913:
3908:
3903:
3899:
3889:
3888:
3887:
3882:
3863:
3860:
3855:
3850:
3846:
3836:
3835:
3834:
3829:
3825:
3821:
3817:
3809:
3803:
3798:
3794:
3792:
3787:
3783:
3781:
3776:
3772:
3767:
3763:
3760:
3758:
3754:
3750:
3742:
3736:
3731:
3727:
3725:
3720:
3716:
3715:
3709:
3707:
3703:
3698:
3692:
3688:
3684:
3679:
3677:
3673:
3669:
3657:
3652:
3645:
3643:
3641:
3637:
3628:
3621:
3605:
3602:
3599:
3596:
3593:
3590:
3587:
3584:
3581:
3578:
3575:
3572:
3565:
3564:
3563:
3561:
3557:
3553:
3549:
3545:
3541:
3537:
3532:
3530:
3526:
3525:tangent lines
3518:
3516:
3514:
3510:
3505:
3503:
3497:
3494:
3490:
3485:
3481:
3477:
3473:
3469:
3465:
3460:
3458:
3454:
3450:
3442:
3440:
3438:
3434:
3433:conic section
3430:
3423:
3421:
3419:
3413:
3405:
3398:
3394:
3391:
3387:
3384:
3383:
3379:
3375:
3372:
3368:
3365:
3364:
3361:
3358:
3356:
3353:
3350:
3349:
3343:
3341:
3337:
3333:
3332:parallelogons
3328:
3326:
3322:
3318:
3314:
3310:
3301:
3294:
3285:
3281:
3276:
3272:
3267:
3263:
3261:
3256:
3252:
3247:
3243:
3241:Figure-eight
3238:
3234:
3226:
3213:
3207:
3205:
3201:
3193:
3187:
3184:
3182:
3177:
3174:
3172:
3168:
3164:
3159:
3156:
3152:
3149:
3144:
3143:
3139:
3135:
3132:
3128:
3125:
3121:
3118:
3114:
3111:
3107:
3104:
3100:
3097:
3093:
3090:
3086:
3085:
3078:
3072:
3070:
3064:
3062:
3059:
3054:
3046:
3041:
3040:
3036:
3032:
3029:
3025:
3022:
3018:
3015:
3011:
3008:
3004:
3001:
2997:
2994:
2990:
2987:
2983:
2982:
2979:
2977:
2973:
2969:
2965:
2960:
2958:
2954:
2950:
2946:
2942:
2938:
2934:
2930:
2925:
2919:
2916:
2911:
2909:
2905:
2897:
2891:
2886:
2878:
2874:
2871:
2867:
2864:
2860:
2857:
2853:
2846:Square faces
2841:
2838:
2837:parallelogons
2831:
2826:
2822:
2819:
2815:
2812:
2808:
2805:
2801:
2793:
2789:
2784:
2781:
2779:
2775:
2774:parallelogons
2771:
2767:
2763:
2757:
2753:
2739:
2735:
2731:
2722:
2718:
2715:
2711:
2708:
2704:
2703:
2696:
2693:
2692:
2686:
2684:
2665:
2661:
2658:
2653:
2634:
2630:
2627:
2597:
2593:
2570:
2566:
2565:
2559:
2549:
2537:
2531:
2525:
2518:
2514:
2509:
2505:
2500:
2496:
2491:
2487:
2482:
2478:
2473:
2469:
2467:
2462:
2458:
2457:
2453:
2450:
2447:
2441:
2437:
2434:
2431:
2428:
2425:
2422:
2419:
2415:
2412:
2411:
2408:
2406:
2402:
2401:parallelogons
2398:
2394:
2390:
2385:
2383:
2379:
2374:
2372:
2371:parallelogons
2368:
2364:
2360:
2356:
2352:
2349:
2345:
2341:
2337:
2333:
2329:
2325:
2321:
2317:
2313:
2308:
2290:
2270:
2262:
2258:
2254:
2250:
2246:
2241:
2234:
2226:
2221:
2209:
2204:
2200:
2198:
2196:
2191:
2187:
2185:
2178:
2174:
2172:
2163:
2159:
2154:
2150:
2148:
2141:
2137:
2130:
2126:
2124:
2117:
2113:
2109:
2104:
2100:
2098:
2094:
2087:
2083:
2081:
2077:
2076:
2072:
2071:
2065:
2049:
2044:
2039:
2035:
2029:
2024:
2021:
2018:
2014:
2010:
2007:
2002:
1997:
1991:
1986:
1982:
1976:
1971:
1968:
1965:
1961:
1956:
1947:
1946:
1945:
1929:
1925:
1901:
1897:
1891:
1887:
1881:
1877:
1873:
1870:
1865:
1860:
1854:
1850:
1846:
1841:
1837:
1832:
1826:
1822:
1819:
1814:
1809:
1805:
1801:
1796:
1791:
1787:
1783:
1778:
1773:
1769:
1765:
1760:
1755:
1751:
1747:
1742:
1737:
1733:
1729:
1724:
1719:
1715:
1707:
1693:
1689:
1683:
1679:
1675:
1670:
1666:
1661:
1657:
1654:
1649:
1644:
1640:
1636:
1631:
1626:
1622:
1618:
1613:
1608:
1604:
1600:
1595:
1590:
1586:
1582:
1577:
1572:
1568:
1564:
1559:
1554:
1550:
1542:
1528:
1524:
1518:
1514:
1510:
1505:
1501:
1496:
1492:
1489:
1484:
1479:
1475:
1471:
1466:
1461:
1457:
1453:
1448:
1443:
1439:
1435:
1430:
1425:
1421:
1417:
1412:
1407:
1403:
1399:
1394:
1389:
1385:
1377:
1376:
1375:
1359:
1355:
1334:
1314:
1302:
1300:
1298:
1294:
1290:
1285:
1278:
1276:
1260:
1257:
1250:
1247:
1240:
1235:
1204:
1199:
1195:
1191:
1188:
1186:
1176:
1169:
1165:
1161:
1158:
1153:
1147:
1142:
1139:
1136:
1133:
1127:
1125:
1115:
1111:
1108:
1102:
1100:
1095:
1084:
1083:
1082:
1066:
1061:
1058:
1055:
1052:
1049:
1046:
1037:
1033:
1029:
1025:
1021:
1018:
1014:
991:
986:
982:
978:
975:
970:
966:
962:
959:
957:
947:
943:
939:
936:
931:
927:
923:
920:
918:
908:
904:
898:
894:
888:
885:
882:
877:
874:
869:
864:
860:
854:
848:
843:
837:
835:
825:
821:
815:
810:
807:
804:
801:
798:
795:
790:
786:
780:
774:
769:
763:
761:
756:
745:
744:
743:
726:
723:
718:
714:
708:
705:
685:
680:
676:
670:
667:
662:
658:
652:
649:
641:
637:
630:
627:
624:
621:
618:
615:
610:
607:
598:
597:
596:
594:
590:
586:
582:
578:
574:
570:
566:
562:
558:
551:= side length
550:
546:
542:
538:
534:
530:
523:
512:
508:
504:
493:
484:
483:Fermat primes
468:
460:
459:
454:
450:
443:
434:
432:
428:
425:
421:
420:tessellations
417:
413:
410:
406:
401:
399:
395:
387:
383:
379:
375:
371:
367:
363:
359:
355:
335:
331:
320:
316:
311:
309:
305:
301:
297:
293:
288:
286:
283:
279:
275:
273:
264:
262:
260:
256:
251:
239:
229:
225:
221:
211:
209:
205:
202:
198:
194:
190:
186:
183:
179:
175:
172:
168:
164:
156:
153:
151:
147:
109:
107:
103:
99:
97:
93:
89:
87:
83:
79:
76:
73:
69:
62:
57:
52:
47:
40:
33:
19:
6417:>20 sides
6352:Decagon (10)
6337:Heptagon (7)
6331:
6327:Pentagon (5)
6317:Triangle (3)
6212:Equidiagonal
6063:
6032:
6023:
6015:
6006:
5997:
5977:10-orthoplex
5713:Dodecahedron
5674:
5634:
5623:
5612:
5603:
5594:
5585:
5581:
5571:
5563:
5559:
5551:
5547:
5493:
5438:
5400:
5396:
5385:. Retrieved
5376:
5372:
5362:
5343:
5335:
5330:
5319:. Retrieved
5310:
5304:
5294:
5286:
5281:
5269:
5248:
5234:cite journal
5207:
5203:
5179:, retrieved
5159:
5152:
5146:Cube picture
5141:
4351:
4283:
4054:Hexagons in
3992:of the form
3944:There is no
3943:
3880:
3878:
3827:
3823:
3815:
3813:
3780:3-3 duoprism
3746:
3699:
3682:
3680:
3675:
3672:skew polygon
3668:skew hexagon
3667:
3665:
3658:, symmetry D
3646:Skew hexagon
3633:
3559:
3555:
3551:
3547:
3543:
3539:
3533:
3522:
3509:circumcircle
3506:
3498:
3492:
3488:
3483:
3479:
3475:
3471:
3467:
3463:
3461:
3446:
3427:
3415:
3329:
3306:
3288:Triple-tail
3279:Double-tail
3250:Center-flip
3197:
3167:skew hexagon
3155:star polygon
2961:
2926:
2912:
2901:
2832:Regular {6}
2755:
2751:
2737:
2728:
2654:
2623:
2451:
2445:
2439:
2435:
2429:
2423:
2417:
2413:
2396:
2392:
2388:
2386:
2377:
2375:
2366:
2358:
2354:
2343:
2331:
2323:
2319:
2315:
2309:
2268:
2266:
2260:
2256:
2252:
2248:
2244:
2232:
2171:parallelogon
1916:
1306:
1289:circumradius
1286:
1279:
1223:
1035:
1031:
1027:
1023:
1019:
1010:
741:
592:
584:
576:
572:
569:circumradius
564:
555:The maximal
554:
548:
540:
537:Circumradius
532:
511:line segment
503:intersection
456:
415:
402:
381:
373:
319:circumcircle
312:
289:
270:
268:
223:
217:
208:Dual polygon
161:), order 2×6
6613:Star-shaped
6588:Rectilinear
6558:Equilateral
6553:Equiangular
6517:Hendecagram
6361:11–20 sides
6342:Octagon (8)
6332:Hexagon (6)
6307:Monogon (1)
6149:Equilateral
5986:10-demicube
5947:9-orthoplex
5897:8-orthoplex
5847:7-orthoplex
5804:6-orthoplex
5774:5-orthoplex
5729:Pentachoron
5717:Icosahedron
5692:Tetrahedron
5379:: 105–114.
5313:: 243–246.
5210:: 335–355.
5074:facets, is
4998:The Hexagon
4943:In French,
4310:Icosahedral
4300:Tetrahedral
4073:Icosahedral
4063:Tetrahedral
3970:soccer ball
3820:equilateral
3325:compression
3307:From bees'
3058:Star figure
3049:t{3} = {6}
2697:projection
2312:John Conway
451:, given by
409:equilateral
398:equilateral
296:equiangular
292:equilateral
193:equilateral
6644:6 (number)
6638:Categories
6618:Tangential
6522:Dodecagram
6300:1–10 sides
6291:By number
6272:Tangential
6252:Right kite
5972:10-simplex
5956:9-demicube
5906:8-demicube
5856:7-demicube
5813:6-demicube
5783:5-demicube
5697:Octahedron
5387:2015-04-12
5321:2014-11-17
5217:2010.12340
5181:2015-11-06
5134:References
4965:Hexagonal
4949:refers to
4946:l'Hexagone
4784:A beehive
4768:Assembled
4531:1-uniform
4305:Octahedral
4068:Octahedral
3950:tessellate
3886:such that
3833:such that
3735:Octahedron
3706:octahedron
3502:concurrent
3309:honeycombs
3270:Fish-tail
3181:octahedron
3178:projection
3073:Alternated
2937:alternated
2924:symmetry.
2835:Hexagonal
2687:Dissection
2225:reflection
524:Parameters
376:) and six
352:times the
308:tangential
181:Properties
6598:Reinhardt
6507:Enneagram
6497:Heptagram
6487:Pentagram
6454:65537-gon
6312:Digon (2)
6282:Trapezoid
6247:Rectangle
6197:Bicentric
6159:Isosceles
6136:Triangles
6020:orthoplex
5942:9-simplex
5892:8-simplex
5842:7-simplex
5799:6-simplex
5769:5-simplex
5738:Tesseract
5440:MathWorld
5435:"Hexagon"
5076:self-dual
5072:orthoplex
4786:honeycomb
4477:Prismoids
3986:truncated
3974:fullerene
3861:≤
3802:5-simplex
3640:centroids
3260:Unicursal
3202:with the
3169:, within
3065:Truncated
3055:Stellated
3047:Truncated
2964:dodecagon
2945:stellated
2933:dodecagon
2929:truncated
2915:truncated
2432:2 (2222)
2348:elongated
2135:directed
2015:∑
1962:∑
1258:≈
1251:π
1189:≈
1137:⋅
976:≈
960:≈
937:≈
921:≈
642:∘
631:
581:inscribed
427:honeycomb
412:triangles
300:bicentric
282:truncated
100:{6}, t{3}
6573:Isotoxal
6568:Isogonal
6512:Decagram
6502:Octagram
6492:Hexagram
6293:of sides
6222:Harmonic
6123:Polygons
6074:Topics:
6037:demicube
6002:polytope
5996:Uniform
5757:600-cell
5753:120-cell
5706:Demicube
5680:Pentagon
5660:Triangle
5488:CGP Grey
5481:animated
5411:Archived
5381:Archived
5351:Archived
5315:Archived
5175:archived
5122:Havannah
5105:Hexagram
5058:See also
4973:minerals
4967:Hanksite
4801:carapace
4754:graphene
4528:Regular
4288:G(2,0):
3980:and the
3366:Regular
3160:Extended
3147:hexagon
2949:hexagram
2353:, while
2336:isotoxal
2328:isogonal
2147:isogonal
2123:isotoxal
2092:regular
2066:Symmetry
1297:diagonal
1293:inradius
589:inradius
561:diagonal
557:diameter
545:Inradius
458:Elements
394:triangle
364:are 120
298:. It is
220:geometry
201:isotoxal
197:isogonal
155:Dihedral
86:vertices
6593:Regular
6538:Concave
6531:Classes
6439:257-gon
6262:Rhombus
6202:Crossed
6011:simplex
5981:10-cube
5748:24-cell
5734:16-cell
5675:Hexagon
5529:regular
5477:YouTube
5274:Coxeter
5064:24-cell
5002:theatre
4842:Benzene
4636:tr{6,3}
4603:rr{6,3}
3976:fame),
3753:regular
3311:to the
3145:Crossed
3075:h{6} =
3067:t{6} =
3042:Regular
2968:squares
2794:Rhombs
2746:⁄
2734:zonogon
2730:Coxeter
2426:(2*22)
2420:(*632)
2351:rhombus
2168:general
1273:of its
1017:apothem
1013:polygon
424:beehive
405:squares
366:degrees
354:apothem
274:hexagon
272:regular
255:polygon
224:hexagon
171:degrees
18:Sexagon
6603:Simple
6548:Cyclic
6543:Convex
6267:Square
6207:Cyclic
6169:Obtuse
6164:Kepler
5951:9-cube
5901:8-cube
5851:7-cube
5808:6-cube
5778:5-cube
5665:Square
5542:Family
5465:Hexnet
5260:
5167:
5036:Taiwan
4890:basalt
4570:r{6,3}
3634:If an
3558:, and
3511:of an
3453:cyclic
2695:6-cube
2448:(22*)
2442:(3*3)
2395:, and
2289:cyclic
1261:0.8270
1034:, and
963:0.6495
453:Euclid
362:angles
304:cyclic
259:simple
226:(from
189:cyclic
185:Convex
6578:Magic
6174:Right
6154:Ideal
6144:Acute
5670:p-gon
5479:– an
5212:arXiv
4770:E-ELT
4537:{6,3}
3670:is a
3451:is a
3351:Form
2454:(××)
2399:, as
2363:kites
2340:duals
2334:, an
2326:, an
2287:), 4
2271:has D
1192:3.464
1081:, so
979:0.866
940:3.464
924:2.598
403:Like
250:gonía
244:γωνία
228:Greek
82:Edges
6608:Skew
6232:Kite
6127:List
6028:cube
5701:Cube
5531:and
5258:ISBN
5240:link
5165:ISBN
5097:: a
5066:: a
4927:The
4020:and
3972:and
3968:(of
3914:>
3724:Cube
3704:and
3702:cube
3700:The
3447:The
3171:cube
3069:{12}
3061:2{3}
3044:{6}
2970:and
2885:Cube
2770:cube
2758:− 1)
2736:(a 2
2357:and
2291:: (Z
2267:The
1347:and
407:and
294:and
276:has
222:, a
212:Self
176:120°
84:and
71:Type
5577:(p)
5475:on
5463:on
5222:doi
5004:in
4896:in
3768:5D
3765:4D
3685:is
3493:bdf
3489:ace
3321:wax
3227:Dih
3221:Dih
3215:Dih
3077:{3}
2843:3D
2791:2D
2544:Dih
2532:Dih
2526:Dih
2521:a1
2512:p2
2503:d2
2494:d2
2485:g2
2476:i4
2466:r12
2446:pmg
2424:cmm
2397:r12
2316:r12
2303:, Z
2299:, Z
2295:, Z
2257:r12
2233:r12
2231:or
2207:a1
2194:g3
2181:p2
2157:d2
2107:i4
2090:r12
1917:If
1291:to
628:cos
455:'s
317:or
238:hex
218:In
6640::
6082:•
6078:•
6058:21
6054:•
6051:k1
6047:•
6044:k2
6022:•
5979:•
5949:•
5927:21
5923:•
5920:41
5916:•
5913:42
5899:•
5877:21
5873:•
5870:31
5866:•
5863:32
5849:•
5827:21
5823:•
5820:22
5806:•
5776:•
5755:•
5736:•
5715:•
5699:•
5631:/
5620:/
5610:/
5601:/
5579:/
5437:.
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5377:15
5375:.
5371:.
5311:14
5309:.
5303:.
5236:}}
5232:{{
5220:.
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5206:.
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5190:^
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3960:,
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3695:3d
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3554:,
3550:,
3546:,
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3504:.
3496:.
3491:=
3482:,
3478:,
3474:,
3470:,
3466:,
3459:.
3327:.
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2166:g2
2144:p6
2133:g6
2120:d6
1284:.
1277:.
1030:=
638:30
591:,
571:,
547:;
543:=
539:;
535:=
514:AB
499:AB
269:A
247:,
235:,
232:ἕξ
199:,
195:,
191:,
187:,
157:(D
6129:)
6125:(
6115:e
6108:t
6101:v
6066:-
6064:n
6056:k
6049:2
6042:1
6035:-
6033:n
6026:-
6024:n
6018:-
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6007:n
6000:-
5998:n
5925:4
5918:2
5911:1
5875:3
5868:2
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5818:1
5647:n
5645:H
5638:2
5635:G
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5624:F
5616:8
5613:E
5607:7
5604:E
5598:6
5595:E
5586:n
5582:D
5575:2
5572:I
5564:n
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5490:.
5457:.
5443:.
5417:.
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5324:.
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5185:.
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3831:1
3828:d
3824:a
3606:.
3603:f
3600:+
3597:d
3594:+
3591:b
3588:=
3585:e
3582:+
3579:c
3576:+
3573:a
3560:f
3556:e
3552:d
3548:c
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3540:a
3484:f
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3472:c
3468:b
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3229:3
3223:1
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2922:3
2756:m
2754:(
2752:m
2748:2
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2550:Z
2546:1
2540:2
2538:Z
2534:2
2528:6
2440:m
2436:p
2430:p
2418:m
2416:6
2414:p
2305:1
2301:2
2297:3
2293:6
2285:2
2283:D
2277:6
2273:6
2263:.
2253:g
2249:p
2245:d
2229:6
2050:.
2045:4
2040:i
2036:d
2030:6
2025:1
2022:=
2019:i
2011:4
2008:=
2003:2
1998:)
1992:2
1987:i
1983:d
1977:6
1972:1
1969:=
1966:i
1957:(
1930:i
1926:d
1902:.
1898:)
1892:2
1888:L
1882:2
1878:R
1874:2
1871:+
1866:2
1861:)
1855:2
1851:L
1847:+
1842:2
1838:R
1833:(
1827:(
1823:3
1820:=
1815:4
1810:6
1806:d
1802:+
1797:4
1792:4
1788:d
1784:+
1779:4
1774:2
1770:d
1766:=
1761:4
1756:5
1752:d
1748:+
1743:4
1738:3
1734:d
1730:+
1725:4
1720:1
1716:d
1694:,
1690:)
1684:2
1680:L
1676:+
1671:2
1667:R
1662:(
1658:3
1655:=
1650:2
1645:6
1641:d
1637:+
1632:2
1627:4
1623:d
1619:+
1614:2
1609:2
1605:d
1601:=
1596:2
1591:5
1587:d
1583:+
1578:2
1573:3
1569:d
1565:+
1560:2
1555:1
1551:d
1529:,
1525:)
1519:2
1515:L
1511:+
1506:2
1502:R
1497:(
1493:2
1490:=
1485:2
1480:6
1476:d
1472:+
1467:2
1462:3
1458:d
1454:=
1449:2
1444:5
1440:d
1436:+
1431:2
1426:2
1422:d
1418:=
1413:2
1408:4
1404:d
1400:+
1395:2
1390:1
1386:d
1360:i
1356:d
1335:L
1315:R
1248:2
1241:3
1236:3
1205:.
1200:2
1196:r
1177:3
1170:2
1166:r
1162:2
1159:=
1154:2
1148:3
1143:r
1140:4
1134:r
1128:=
1116:2
1112:p
1109:a
1103:=
1096:A
1067:3
1062:r
1059:4
1056:=
1053:R
1050:6
1047:=
1036:p
1032:r
1028:a
1024:p
1020:a
992:.
987:2
983:d
971:2
967:D
948:2
944:r
932:2
928:R
909:2
905:d
899:2
895:3
889:=
886:d
883:D
878:4
875:3
870:=
865:2
861:D
855:8
849:3
844:3
838:=
826:2
822:r
816:3
811:2
808:=
805:r
802:R
799:3
796:=
791:2
787:R
781:2
775:3
770:3
764:=
757:A
727:.
724:D
719:2
715:3
709:=
706:d
686:t
681:2
677:3
671:=
668:R
663:2
659:3
653:=
650:R
647:)
634:(
625:=
622:r
619:=
616:d
611:2
608:1
593:r
585:d
577:t
573:R
565:D
549:t
541:r
533:R
485:.
469:=
390:6
388:D
380:(
372:(
336:3
332:2
173:)
169:(
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48:.
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