# Truncated pentagonal hexecontahedron

Truncated pentagonal hexecontahedron Conway t5gD or wD
Goldberg {5+,3}2,1
Fullerene C140
Faces 72:
60 hexagons
12 pentagons
Edges 210
Vertices 140
Symmetry group Icosahedral (I)
Dual polyhedron Pentakis snub dodecahedron
Properties convex, chiral

The truncated pentagonal hexecontahedron is a convex polyhedron with 72 faces: 60 hexagons and 12 pentagons triangular, with 210 edges, and 140 vertices. Its dual is the pentakis snub dodecahedron.

It is Goldberg polyhedron {5+,3}2,1 in the icosahedral family, with chiral symmetry. The relationship between pentagons steps into 2 hexagons away, and then a turn with one more step.

It is a Fullerene C140.

## Construction

It is explicitly called a pentatruncated pentagonal hexecontahedron since only the valence-5 vertices of the pentagonal hexecontahedron are truncated. Its topology can be constructed in Conway polyhedron notation as t5gD and more simply wD as a whirled dodecahedron, 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. ## Related polyhedra

The whirled dodecahedron creates more polyhedra by basic Conway polyhedron notation. 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).

## See also

• Truncated pentagonal icositetrahedron t4gC