Icositruncated dodecadodecahedron

Template:Short description Template:Uniform polyhedra db File:Icositruncated dodecadodecahedron.stl In geometry, the icositruncated dodecadodecahedron or icosidodecatruncated icosidodecahedron is a nonconvex uniform polyhedron, indexed as U₄₅.

Convex hull

Its convex hull is a nonuniform truncated icosidodecahedron.

Truncated icosidodecahedron

Convex hull

Icositruncated dodecadodecahedron

Cartesian coordinates

Cartesian coordinates for the vertices of an icositruncated dodecadodecahedron are all the even permutations of $$\begin{array}{ccccc}(& \pm [2-\frac{1}{\phi }],& \pm 1,& \pm [2+\phi ]& ),\\ (& \pm 1,& \pm \frac{1}{{\phi }^2},& \pm [3\phi -1]& ),\\ (& \pm 2,& \pm \frac{2}{\phi },& \pm 2\phi & ),\\ (& \pm 3,& \pm \frac{1}{{\phi }^2},& \pm {\phi }^2& ),\\ (& \pm {\phi }^2,& \pm 1,& \pm [3\phi -2]& ),\end{array}$$

where $\phi =\frac{1+\sqrt{5}}{2}$ is the golden ratio.

Related polyhedra

Tridyakis icosahedron

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

See also

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

References

• Template:Citation Photo on page 96, Dorman Luke construction and stellation pattern on page 97.

External links

• Template:Mathworld

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