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{{Uniform polyhedra db|Uniform dual polyhedron stat table|gID}}
In [[geometry]], the '''great rhombic triacontahedron''' is a nonconvex [[Isohedral figure|isohedral]], [[isotoxal]] [[polyhedron]]. It is the [[Dual polyhedron|dual]] of the [[great icosidodecahedron]] (U54). It has 30 intersecting [[rhombus|rhombic]] faces.


The great rhombic triacontahedron can be constructed by expanding the size of the faces of a [[rhombic triacontahedron]] by a factor of <math>\varphi^3=1+2\varphi\!</math>, with <math>\varphi\!</math> being the [[golden ratio]].
==References==
*{{Citation | last1=Wenninger | first1=Magnus | author1-link=Magnus Wenninger | title=Dual Models | publisher=[[Cambridge University Press]] | isbn=978-0-521-54325-5 | id={{MathSciNet | id = 730208}} | year=1983}}


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==External links==
* {{mathworld | urlname = GreatRhombicTriacontahedron| title =Great rhombic triacontahedron}}
* [http://gratrix.net/polyhedra/uniform/summary Uniform polyhedra and duals]
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Revision as of 20:28, 11 November 2013

Template:Uniform polyhedra db In geometry, the great rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron. It is the dual of the great icosidodecahedron (U54). It has 30 intersecting rhombic faces.

The great rhombic triacontahedron can be constructed by expanding the size of the faces of a rhombic triacontahedron by a factor of φ3=1+2φ, with φ being the golden ratio.

References

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  • Uniform polyhedra and duals

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