Icositruncated dodecadodecahedron

Its convex hull is a nonuniform truncated icosidodecahedron.

Cartesian coordinates for the vertices of an icositruncated dodecadodecahedron are all the even permutations of

$$\backslash begin\{array\}\{crrlc\}$$

\Bigl(& \pm\bigl[2-\frac{1}{\varphi}\bigr],& \pm\,1,& \pm\bigl[2+\varphi\bigr] &\Bigr), \\

\Bigl(& \pm\,1,& \pm\,\frac{1}{\varphi^2},& \pm\bigl[3\varphi-1\bigr] &\Bigr), \\

\Bigl(& \pm\,2,& \pm\,\frac{2}{\varphi},& \pm\,2\varphi &\Bigr), \\

\Bigl(& \pm\,3,& \pm\,\frac{1}{\varphi^2},& \pm\,\varphi^2 &\Bigr), \\

\Bigl(& \pm\,\varphi^2,& \pm\,1,& \pm\bigl[3\varphi-2\bigr] &\Bigr),

\end{array}

where $\backslash varphi\; =\; \backslash tfrac\{1+\backslash sqrt\; 5\}\{2\}$ is the golden ratio.

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The tridyakis icosahedron is the dual polyhedron of the icositruncated dodecadodecahedron. It has 44 vertices, 180 edges, and 120 scalene triangular faces.

• Catalan solid Duals to convex uniform polyhedra
• Uniform polyhedra
• List of uniform polyhedra

• {{Citation | last1=Wenninger | first1=Magnus | author1-link=Magnus Wenninger | title=Dual Models | publisher=Cambridge University Press | isbn=978-0-521-54325-5 |mr=730208 | year=1983}} Photo on page 96, Dorman Luke construction and stellation pattern on page 97.

• {{mathworld | urlname = IcositruncatedDodecadodecahedron| title = Icositruncated dodecadodecahedron}}

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Category:Uniform polyhedra

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