The pentagonal hexecontahedron is the 60-faced dual polyhedron of the snub dodecahedron (Holden 1971, p. 55). It is Wenninger dual .

Its irregular pentagonal faces have vertex angles of

			(1)
			(2)
			(3)

(four times) and

			(4)
			(5)

(once), where is a polynomial root.

Because it is the dual of the chiral snub dodecahedron, the pentagonal hexecontahedron also comes in two enantiomorphous forms, known as laevo (left) and dextro (right). An attractive dual of the two enantiomers superposed on one another is illustrated above.

Starting with a snub dodecahedron with unit edge lengths, the edges lengths of the pentagonal hexecontahedron are given by the roots of

	(6)
	(7)

which have approximate values and .

The surface area and volume are both given by the roots of 12th-order polynomial with large coefficients. They have approximate values and .

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

Wenninger, M. J. Dual Models. Cambridge, England: Cambridge University Press, p. 29, 1983.

CITE THIS AS:

Weisstein, Eric W. "Pentagonal Hexecontahedron." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PentagonalHexecontahedron.html