dodecahedron is the 60-faced dual polyhedron of
the truncated icosahedron (Holden 1971, p. 55). It is Wenninger dual . It can be constructed by augmentation
of a unit edge-length dodecahedron by a pyramid
with height .
tetrahedron 10-compound, cube 5-compound, icosahedron, and dodecahedron
can be inscribed in the vertices of the pentakis dodecahedron (E. Weisstein,
Dec. 25-27, 2009).
The pentakis dodecahedron is he convex hull of the small triambic icosahedron hull.
Taking the dual of a
with unit edge lengths gives a pentakis dodecahedron with edge lengths
Normalizing so that
, the surface area and
See also Archimedean Dual
Pentakis Dodecahedral Graph
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References Holden, A. New York: Columbia University Press, p. 55, 1971. Shapes, Space, and Symmetry. Kabai,
S. Mathematical Graphics I: Lessons in Computer Graphics Using Mathematica.
Püspökladány, Hungary: Uniconstant, p. 153, 2002. Wenninger,
Cambridge, England: Cambridge University Press, p. 18, 1983. Dual
Models. Cite this as:
Weisstein, Eric W. "Pentakis Dodecahedron."
From --A Wolfram Web Resource. MathWorld https://mathworld.wolfram.com/PentakisDodecahedron.html