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361:, being in the Euclidean plane for n=6, and hyperbolic plane for any higher n. The series can be considered to begin with n=2, with one set of faces degenerated into
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687:
Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms.
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KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
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Drawn in chiral pairs, with edges missing between black triangles:
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is a semiregular tiling of the hyperbolic plane. There are four
259:
is another related hyperbolic tiling with Schläfli symbol
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1611:
684:
that can be based from the regular heptagonal tiling.
1461:"Chapter 10: Regular honeycombs in hyperbolic space".
1457:(Chapter 19, The Hyperbolic Archimedean Tessellations)
357:. These figures and their duals have (n32) rotational
92:
318:
This semiregular tiling is a member of a sequence of
83:
26:
116:{\displaystyle s{\begin{Bmatrix}7\\3\end{Bmatrix}}}
322:polyhedra and tilings with vertex figure (3.3.3.3.
115:
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389:
8:
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1582:Hyperbolic Planar Tessellations, Don Hatch
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367:
87:
82:
1445:, Heidi Burgiel, Chaim Goodman-Strauss,
1572:Hyperbolic and Spherical Tiling Gallery
697:
374:32 symmetry mutations of snub tilings:
1463:The Beauty of Geometry: Twelve Essays
694:Uniform heptagonal/triangular tilings
7:
1649:
1647:
1592:
1590:
1667:. You can help Knowledge (XXG) by
1610:. You can help Knowledge (XXG) by
295:order-7-3 floret pentagonal tiling
207:Order-7-3 floret pentagonal tiling
25:
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1517:List of uniform planar tilings
233:order-3 snub heptagonal tiling
1:
314:Related polyhedra and tilings
293:The dual tiling is called an
1465:. Dover Publications. 1999.
1512:Tilings of regular polygons
680:there are eight hyperbolic
257:snub tetraheptagonal tiling
1760:
1646:
1589:
1558:"Poincaré hyperbolic disk"
1089:
692:
30:Snub triheptagonal tiling
1507:Order-3 heptagonal tiling
724:
426:
416:
406:
370:
56:Hyperbolic uniform tiling
34:
29:
1500:Floret pentagonal tiling
1447:The Symmetries of Things
299:floret pentagonal tiling
297:, and is related to the
1606:-related article is a
328:Coxeter–Dynkin diagram
117:
18:Snub heptagonal tiling
1744:Stereochemistry stubs
1739:Metric geometry stubs
1495:Snub hexagonal tiling
118:
678:Wythoff construction
81:
63:Vertex configuration
1729:Semiregular tilings
1604:hyperbolic geometry
1539:"Hyperbolic tiling"
427:Compact hyperbolic
42:Poincaré disk model
1719:Hyperbolic tilings
1555:Weisstein, Eric W.
1536:Weisstein, Eric W.
113:
107:
1676:
1675:
1619:
1618:
1455:978-1-56881-220-5
1434:
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674:
673:
670:V3.3.3.3.∞
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217:Vertex-transitive
16:(Redirected from
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1724:Isogonal tilings
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46:hyperbolic plane
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1661:stereochemistry
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682:uniform tilings
572:
565:3.3.3.3.∞
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249:Schläfli symbol
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138:Coxeter diagram
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73:Schläfli symbol
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1714:Chiral figures
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1528:External links
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1522:Kagome lattice
1519:
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1490:
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1471:
1458:
1443:John H. Conway
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1090:Uniform duals
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1663:article is a
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132:| 7 3 2
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1734:Snub tilings
1669:expanding it
1658:
1612:expanding it
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686:
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226:
667:V3.3.3.3.8
664:V3.3.3.3.7
289:Dual tiling
77:sr{7,3} or
1708:Categories
1437:References
1429:V3.3.3.3.7
725:Symmetry:
660:V3.3.3.3.6
655:V3.3.3.3.5
650:V3.3.3.3.4
645:V3.3.3.3.3
640:V3.3.3.3.2
456:∞32
430:Paracomp.
213:Properties
67:3.3.3.3.7
1563:MathWorld
1544:MathWorld
560:3.3.3.3.8
555:3.3.3.3.7
550:3.3.3.3.6
545:3.3.3.3.5
540:3.3.3.3.4
535:3.3.3.3.3
530:3.3.3.3.2
423:Euclidean
418:Spherical
376:3.3.3.3.n
247:. It has
237:triangles
1489:See also
1481:99035678
1417:V3.4.7.4
1400:V3.7.3.7
1395:V3.14.14
728:, (*732)
573:figures
463:figures
407:Symmetry
359:symmetry
243:on each
241:heptagon
239:and one
229:geometry
196:, (732)
1423:V4.6.14
1083:sr{7,3}
1076:tr{7,3}
1069:rr{7,3}
734:, (732)
676:From a
635:Config.
525:Config.
320:snubbed
261:sr{7,4}
255:. The
253:sr{7,3}
44:of the
1479:
1469:
1453:
1449:2008,
1405:V6.6.7
1055:t{3,7}
1048:r{7,3}
1041:t{7,3}
363:digons
326:) and
267:Images
245:vertex
231:, the
220:Chiral
1659:This
1602:This
1062:{3,7}
1034:{7,3}
1665:stub
1608:stub
1477:LCCN
1467:ISBN
1451:ISBN
571:Gyro
461:Snub
453:832
450:732
447:632
444:532
441:432
438:332
435:232
202:Dual
52:Type
251:of
227:In
169:or
1710::
1560:.
1541:.
1475:.
1411:V3
1389:V7
413:32
365:.
301:.
263:.
1696:e
1689:t
1682:v
1671:.
1639:e
1632:t
1625:v
1614:.
1566:.
1547:.
1483:.
715:e
708:t
701:v
411:n
397:e
390:t
383:v
372:n
324:n
109:}
103:3
96:7
90:{
85:s
20:)
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