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230:, reducing original pentagonal faces and adding 5 distorted hexagons around each, in clockwise or counter-clockwise forms. This picture shows its flat construction before the geometry is adjusted into a more spherical form. The snub can create a (5,3) geodesic polyhedron by k5k6.
251:. The zip whirled dodecahedron makes a chamfered truncated icosahedron, and Goldberg (4,1). Whirl applied twice produces Goldberg (5,3), and applied twice with reverse orientations produces goldberg (7,0).
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in the icosahedral family, with chiral symmetry. The relationship between pentagons steps into 2 hexagons away, and then a turn with one more step.
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Fourth class of convex equilateral polyhedron with polyhedral symmetry related to fullerenes and viruses
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Shaping Space: Exploring
Polyhedra in Nature, Art, and the Geometrical Imagination
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The whirled dodecahedron creates more polyhedra by basic
630:"Giant Spherical Cluster with I-C140 Fullerene Topology"
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156:: 60 hexagons and 12 pentagons triangular, with 210
759:"Mathematical Impressions: Goldberg Polyhedra"
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19:Order-5 truncated pentagonal hexecontahedron
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772:, Early Edition doi: 10.1073/pnas.1310939111
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143:order-5 truncated pentagonal hexecontahedron
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198:since only the valence-5 vertices of the
196:pentatruncated pentagonal hexecontahedron
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768:, Stan Schein and James Maurice Gaye,
634:Angewandte Chemie International Edition
620:
695:"A class of multi-symmetric polyhedra"
606:Truncated pentagonal icositetrahedron
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727:(2nd ed.). Springer. pp.
214:Its topology can be constructed in
816:. You can help Knowledge (XXG) by
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715:(2012). "Goldberg Polyhedra". In
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255:Whirled dodecahedron polyhedra
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737:10.1007/978-0-387-92714-5_9
700:Tohoku Mathematical Journal
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787:Conway polyhedron notation
693:Goldberg, Michael (1937).
249:Conway polyhedron notation
216:Conway polyhedron notation
200:pentagonal hexecontahedron
194:It is explicitly called a
166:pentakis snub dodecahedron
123:Pentakis snub dodecahedron
783:VRML polyhedral generator
628:Heinl, Sebastian (2015).
812:-related article is a
761:. Simons Science News.
646:10.1002/anie.201505516
228:whirled dodecahedron
640:(45): 13431–13435.
459:dual whirl-reverse
256:
173:Goldberg polyhedron
868:Pentagonal tilings
863:Goldberg polyhedra
717:Senechal, Marjorie
681:Goldberg polyhedra
679:, 2013, Chapter 9
254:
164:. Its dual is the
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757:(June 18, 2013).
746:978-0-387-92713-8
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243:Related polyhedra
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118:Dual polyhedron
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723:Shaping Space
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421:wrwD = G(7,0)
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79:12 pentagons
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873:Snub tilings
818:expanding it
807:
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785:Try "t5gI" (
755:Hart, George
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713:Hart, George
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453:dual chamfer
408:wwD = G(5,3)
395:cwD = G(4,2)
343:zwD = G(4,1)
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195:
193:
190:Construction
181:
170:
142:
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109:
304:wD = G(2,1)
106:Icosahedral
77:60 hexagons
878:Fullerenes
857:Categories
810:polyhedron
707:: 104–108.
615:References
456:dual whirl
160:, and 140
150:polyhedron
129:Properties
184:Fullerene
135:, chiral
60:Fullerene
664:26411255
600:See also
267:truncate
182:It is a
162:vertices
152:with 72
92:Vertices
47:Goldberg
38:t5gD or
719:(ed.).
655:4691335
287:chamfer
743:
731:–138.
662:
652:
447:medial
438:needle
275:expand
260:"seed"
186:C140.
175:{5+,3}
171:It is
147:convex
133:convex
51:{5+,3}
34:Conway
808:This
592:dwrwD
589:dwrwD
444:ortho
290:whirl
279:bevel
226:as a
158:edges
154:faces
145:is a
84:Edges
72:Faces
814:stub
770:PNAS
741:ISBN
660:PMID
609:t4gC
579:dwwD
576:dwwD
566:dcwD
563:dcwD
450:gyro
435:join
431:dual
424:wrwD
283:snub
263:ambo
220:t5gD
141:The
95:140
87:210
733:doi
729:125
650:PMC
642:doi
553:gwD
550:gwD
540:mwD
537:mwD
527:owD
524:owD
514:kwD
511:kwD
501:nwD
498:nwD
488:jwD
485:jwD
475:dwD
471:dwD
441:kis
411:wwD
398:cwD
385:swD
382:swD
372:bwD
369:bwD
359:ewD
356:ewD
346:zwD
333:twD
330:twD
320:awD
317:awD
271:zip
218:as
177:2,1
75:72:
66:140
53:2,1
859::
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307:wD
224:wD
168:.
112:)
40:wD
845:e
838:t
831:v
820:.
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735::
666:.
644::
110:I
108:(
64:C
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