Truncated pentakis dodecahedron explained

bgcolor=#e7dcc3 colspan=2	Truncated pentakis dodecahedron
align=center colspan=2
Conway notation	tkD
Goldberg polyhedron	GPV(3,0) or 3,0
Fullerene	C180^[1]
Faces	92: 12 pentagons 20+60 hexagons
Edges	270 (2 types)
Vertices	180 (2 types)
Vertex configuration	(60) 5.6.6 (120) 6.6.6
Symmetry group	Icosahedral (Ih)
Dual polyhedron	Hexapentakis truncated icosahedron
Properties	convex

The truncated pentakis dodecahedron is a convex polyhedron constructed as a truncation of the pentakis dodecahedron. It is Goldberg polyhedron G_V(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:

See also

• Near-miss Johnson solid
• Truncated tetrakis cube

References

• .
• 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

• VTML polyhedral generator Try "tkD" (Conway polyhedron notation)

Notes and References

1. http://www.nanotube.msu.edu/fullerene/fullerene.php?C=180 C180 Isomers