Editing Deltoidal hexecontahedron (section)

{{Short description|Catalan solid with 60 faces}}
{|style="float: right; border: 1px solid #BBB; margin: .5em 0 0 .5em;"
!bgcolor=#e7dcc3 colspan=2|Deltoidal hexecontahedron
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|align=center colspan=2|[[Image:deltoidalhexecontahedron.jpg|240px|Deltoidal hexecontahedron]]<br>[[:image:deltoidalhexecontahedron.gif|''(Click here for rotating model)'']]
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|bgcolor=#e7dcc3|Type||[[Catalan solid|Catalan]]
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|bgcolor=#e7dcc3|[[Conway polyhedron notation|Conway notation]]||oD or deD
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|bgcolor=#e7dcc3|[[Coxeter diagram]]||{{CDD|node_f1|5|node|3|node_f1}}
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|bgcolor=#e7dcc3|Face polygon||[[File:DU27 facets.png|60px]]<BR>[[kite (geometry)|kite]]
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|bgcolor=#e7dcc3|Faces||60
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|bgcolor=#e7dcc3|Edges||120
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|bgcolor=#e7dcc3|Vertices||62 = 12 + 20 + 30
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|bgcolor=#e7dcc3|[[Face configuration]]||V3.4.5.4
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|bgcolor=#e7dcc3|[[List of spherical symmetry groups|Symmetry group]]||[[Icosahedral symmetry|I<sub>h</sub>]], H<sub>3</sub>, [5,3], (*532)
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|bgcolor=#e7dcc3|[[Point groups in three dimensions#Rotation groups|Rotation group]]||I, [5,3]<sup>+</sup>, (532)
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|bgcolor=#e7dcc3|[[Dihedral angle]]||154.1214°<br><math>\arccos(\frac{-19-8\sqrt{5}}{41})</math>
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|bgcolor=#e7dcc3|Properties||convex, [[face-transitive]]
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|valign=top align=center|[[Image:Small rhombicosidodecahedron.png|120px]]<BR>[[rhombicosidodecahedron]]<BR>([[dual polyhedron]])
|align=center|[[Image:deltoidalhexecontahedron net.png|120px|Deltoidal hexecontahedron net]]<BR>[[Net (polyhedron)|Net]]
|}
[[File:Deltoidal hexecontahedron.stl|thumb|3D model of a deltoidal hexecontahedron]]
In [[geometry]], a '''deltoidal hexecontahedron''' (also sometimes called a ''trapezoidal hexecontahedron'', a ''strombic hexecontahedron'', or a ''tetragonal hexacontahedron''<ref>Conway, Symmetries of things, p.284-286</ref>) is a [[Catalan solid]] which is the [[dual polyhedron]] of the [[rhombicosidodecahedron]], an [[Archimedean solid]]. It is one of six Catalan solids to not have a [[Hamiltonian path]] among its vertices.<ref>{{Cite web|url=http://mathworld.wolfram.com/ArchimedeanDualGraph.html|title=Archimedean Dual Graph}}</ref>

It is topologically identical to the nonconvex [[rhombic hexecontahedron]].