Truncated pentakis dodecahedron

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.

Truncated pentakis dodecahedron
Conway notationtkD
Goldberg polyhedronGPV(3,0) or {5+,3}3,0
FullereneC180[1]
Faces92:
12 pentagons
20+60 hexagons
Edges270 (2 types)
Vertices180 (2 types)
Vertex configuration(60) 5.6.6
(120) 6.6.6
Symmetry groupIcosahedral (Ih)
Dual polyhedronPentahexakis truncated icosahedron
Propertiesconvex

It is in an infinite sequence of Goldberg polyhedra:

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)...
Image
D

kD

tkD
Duals
I

cD

ktI

See also

References

  • Deza, A.; Deza, M.; Grishukhin, V. (1998), "Fullerenes and coordination polyhedra versus half-cube embeddings", Discrete Mathematics, 192 (1): 41–80, doi:10.1016/S0012-365X(98)00065-X, archived from the original on 2007-02-06.
  • Antoine Deza, Michel Deza, Viatcheslav Grishukhin, Fullerenes and coordination polyhedra versus half-cube embeddings, 1998 PDF
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