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| {{Uniform polyhedra db|Uniform polyhedron stat table|gdID}}
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| In [[geometry]], the '''great [[Ditrigonary polyhedra|ditrigonal]] icosidodecahedron''' is a [[nonconvex uniform polyhedron]], indexed as U<sub>47</sub>. It has 4 [[Schwarz triangle]] equivalent constructions, for example [[Wythoff symbol]] '''3 | 3/2 5''', and [[Coxeter diagram]] [[File:Great ditrigonal icosidodecahedron cd.png]].
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| Its [[circumradius]] is <math>\frac{\sqrt{3}}{2}</math> times the length of its edge,<ref name=Weisstein2003>{{Citation
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| | last = Weisstein | first = Eric W
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| | year = 2003
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| | title = CRC concise encyclopedia of mathematics
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| | isbn = 1-58488-347-2
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| | publisher = Chapman & Hall/CRC
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| | location = Boca Raton
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| }}</ref> a value it shares with the [[cube]].
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| == Related polyhedra ==
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| Its [[convex hull]] is a regular [[dodecahedron]]. It additionally shares its [[edge arrangement]] with the [[small ditrigonal icosidodecahedron]] (having the triangular faces in common), the [[ditrigonal dodecadodecahedron]] (having the pentagonal faces in common), and the regular [[compound of five cubes]].
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| {| class="wikitable" width="400" style="vertical-align:top;text-align:center"
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| |align=center|[[File:Small ditrigonal icosidodecahedron.png|100px]]<BR>[[Small ditrigonal icosidodecahedron]]
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| |align=center|[[File:Great ditrigonal icosidodecahedron.png|100px]]<BR>Great ditrigonal icosidodecahedron
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| |align=center|[[File:Ditrigonal dodecadodecahedron.png|100px]]<BR>[[Ditrigonal dodecadodecahedron]]
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| |-
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| |align=center|[[File:Dodecahedron.png|100px]]<BR>[[Dodecahedron]] ([[convex hull]])
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| |align=center|[[File:Compound of five cubes.png|100px]]<BR>[[Compound of five cubes]]
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| |}
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| == References ==
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| <references/>
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| == External links ==
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| * [[VRML]] model: [http://www.physics.orst.edu/~bulatov/polyhedra/uniform/u52.html]
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| * [http://mathworld.wolfram.com/GreatDitrigonalIcosidodecahedron.html MathWorld]
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| [[Category:Polyhedra]]
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| {{Polyhedron-stub}}
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