Nonconvex great rhombicosidodecahedron

Cartesian coordinates for the vertices of a nonconvex great rhombicosidodecahedron are all the even permutations of

$$\backslash begin\{array\}\{ccclc\}$$

\Bigl(& \pm\,\frac{1}{\varphi^2},& 0,& \pm \bigl[2-\frac{1}{\varphi}\bigr] &\Bigr) \\

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

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

\end{array}

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

It shares its vertex arrangement with the truncated great dodecahedron, and with the uniform compounds of 6 or 12 pentagonal prisms. It additionally shares its edge arrangement with the great dodecicosidodecahedron (having the triangular and pentagrammic faces in common), and the great rhombidodecahedron (having the square faces in common).

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{{Uniform polyhedra db|Uniform dual polyhedron stat table|ugrID}}

File:Great deltoidal hexecontahedron.stl

The great deltoidal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the nonconvex great rhombicosidodecahedron. It is visually identical to the great rhombidodecacron. It has 60 intersecting cross quadrilateral faces, 120 edges, and 62 vertices.

It is also called a great strombic hexecontahedron.

• List of uniform polyhedra

{{Reflist}}

• {{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 | doi=10.1017/CBO9780511569371}}

• {{mathworld | urlname = UniformGreatRhombicosidodecahedron| title = Great rhombicosidodecahedron}}
• {{mathworld | urlname = GreatDeltoidalHexecontahedron| title =Great deltoidal hexecontahedron}}
• [https://web.archive.org/web/20171110075259/http://gratrix.net/polyhedra/uniform/summary/ Uniform polyhedra and duals]

{{Nonconvex polyhedron navigator}}

Category:Uniform polyhedra