The pentakis dodecahedron is the 60-faced dual polyhedron of the truncated icosahedron (Holden 1971, p. 55). It is Wenninger dual . It can be constructed by cumulation of a unit edge-length dodecahedron by a pyramid with height .

Taking the dual of a truncated icosahedron with unit edge lengths gives a pentakis dodecahedron with edge lengths

			(1)
			(2)

Normalizing so that , the surface area and volume are

			(3)
			(4)

Holden, A. Shapes, Space, and Symmetry. New York: Columbia University Press, p. 55, 1971.

Kabai, S. Mathematical Graphics I: Lessons in Computer Graphics Using Mathematica. Püspökladány, Hungary: Uniconstant, p. 153, 2002.

Wenninger, M. J. Dual Models. Cambridge, England: Cambridge University Press, p. 18, 1983.

CITE THIS AS:

Weisstein, Eric W. "Pentakis Dodecahedron." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PentakisDodecahedron.html