Editing Triaugmented truncated dodecahedron

{{Short description|71st Johnson solid}}
{{Infobox polyhedron
|image=triaugmented_truncated_dodecahedron.png
|type=[[Johnson solid|Johnson]]<br>{{math|[[metabiaugmented truncated dodecahedron|''J''{{sub|70}}]] – '''''J''{{sub|71}}''' – [[gyrate rhombicosidodecahedron|''J''{{sub|72}}]]}}
|faces=2+3x3+4x6 [[triangle]]s <br> 3+2x6 [[square (geometry)|square]]s <br> 3 [[pentagon]]s <br> 3x3 [[decagon]]s
|edges=135
|vertices=75
|symmetry={{math|''C''{{sub|3v}}}}
|vertex_config={{math|4x3+3x6(3.10{{sup|2}})<br>3+2x6(3.4.5.4)<br>5x6(3.4.3.10)}}
|dual=-
|properties=[[convex polytope|convex]]
|net=Johnson solid 71 net.png
}}

In [[geometry]], the '''triaugmented truncated dodecahedron''' is one of the [[Johnson solid]]s ({{math|''J''{{sub|71}}}}); of them, it has the greatest volume in proportion to the cube of the side length, as well as the greatest number of edges. As its name suggests, it is created by attaching three [[pentagonal cupola]]s ({{math|''J''{{sub|5}}}}) onto three nonadjacent [[decagon]]al faces of a [[truncated dodecahedron]].

{{Johnson solid}}

==External links==
* {{Mathworld2 | urlname2 = JohnsonSolid | title2 = Johnson solid | urlname =TriaugmentedTruncatedDodecahedron| title =   Triaugmented truncated dodecahedron}}

[[Category:Johnson solids]]
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