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truncated pentakis dodecahedron

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!bgcolor=#e7dcc3 colspan=2|Truncated pentakis dodecahedron

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bgcolor=#e7dcc3|Conway notation[https://levskaya.github.io/polyhedronisme/?recipe=A10tkD tkD]
bgcolor=#e7dcc3|Goldberg polyhedronGPV(3,0) or {5+,3}3,0
bgcolor=#e7dcc3|FullereneC180[http://www.nanotube.msu.edu/fullerene/fullerene.php?C=180 C180 Isomers]
bgcolor=#e7dcc3|Faces92:
12 pentagons
20+60 hexagons
bgcolor=#e7dcc3|Edges270 (2 types)
bgcolor=#e7dcc3|Vertices180 (2 types)
bgcolor=#e7dcc3|Vertex configuration(60) 5.6.6
(120) 6.6.6
bgcolor=#e7dcc3|Symmetry groupIcosahedral (Ih)
bgcolor=#e7dcc3|Dual polyhedronHexapentakis truncated icosahedron
bgcolor=#e7dcc3|Propertiesconvex

The truncated pentakis dodecahedron is a convex polyhedron constructed as a truncation of the pentakis dodecahedron. It is Goldberg polyhedron GV(3,0), with pentagonal faces separated by an edge-direct distance of 3 steps.

Related polyhedra

It is in an infinite sequence of Goldberg polyhedra:

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!Index

!GP(1,0)

!GP(2,0)

!GP(3,0)

!GP(4,0)

!GP(5,0)

!GP(6,0)

!GP(7,0)

!GP(8,0)...

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!Image

|60px
D

|60px
kD

|60px
tkD

|60px

|60px

|60px

|60px

|60px

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!Duals

|60px
I

|60px
cD

|60px
ktI

|60px

|

|60px

|

|

See also

  • Near-miss Johnson solid
  • [https://levskaya.github.io/polyhedronisme/?recipe=tkC&palette=%23ffffff Truncated tetrakis cube]

References

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  • {{citation | last1 = Deza | first1 = A. | last2 = Deza | first2 = M. | author2-link = Michel Deza | last3 = Grishukhin | first3 = V. | title = Fullerenes and coordination polyhedra versus half-cube embeddings | journal = Discrete Mathematics | volume = 192 | issue = 1 | year = 1998 | pages = 41–80 | url = http://www.ehess.fr/centres/cams/papers/144.ps.gz | doi = 10.1016/S0012-365X(98)00065-X | url-status = dead | archiveurl = https://web.archive.org/web/20070206064633/http://www.ehess.fr/centres/cams/papers/144.ps.gz | archivedate = 2007-02-06 | doi-access = free }}.
  • Antoine Deza, Michel Deza, Viatcheslav Grishukhin, Fullerenes and coordination polyhedra versus half-cube embeddings, 1998 PDF [http://www.cas.mcmaster.ca/~deza/dm1998.pdf]

External links

  • [http://www.georgehart.com/virtual-polyhedra/conway_notation.html VTML polyhedral generator] Try "tkD" (Conway polyhedron notation)

Category:Goldberg polyhedra