Editing Parabiaugmented dodecahedron

{{Short description|59th Johnson solid}}
{{Infobox polyhedron
|image=parabiaugmented_dodecahedron.png
|type=[[Johnson solid|Johnson]]<br>{{math|[[augmented dodecahedron|''J''{{sub|58}}]] – '''''J''{{sub|59}}''' – [[metabiaugmented dodecahedron|''J''{{sub|60}}]]}}
|faces=10 [[triangle]]s <br> 10 [[pentagon]]s
|edges=40
|vertices=22
|symmetry={{math|''D''{{sub|5d}}}}
|vertex_config={{math|10(5{{sup|3}})<br>10(3{{sup|2}}.5{{sup|2}})<br>2(3{{sup|5}})}}
|dual=[[Gyroelongated pentagonal bifrustum]]
|properties=[[convex polytope|convex]]
|net=Johnson solid 59 net.png
}}

In [[geometry]], the '''parabiaugmented dodecahedron''' is one of the [[Johnson solid]]s ({{math|''J''{{sub|59}}}}). It can be seen as a [[dodecahedron]] with two [[pentagonal pyramid]]s ({{math|''J''{{sub|2}}}}) attached to opposite faces. When pyramids are attached to a dodecahedron in other ways, they may result in an [[augmented dodecahedron]] ({{math|''J''{{sub|58}}}}), a [[metabiaugmented dodecahedron]] ({{math|''J''{{sub|60}}}}), a [[triaugmented dodecahedron]] ({{math|''J''{{sub|61}}}}), or even a [[pentakis dodecahedron]] if the faces are made to be irregular.

The dual of this solid is the [[Gyroelongated pentagonal bifrustum]].
{{Johnson solid}}

==External links==
* {{MathWorld2 | urlname2=JohnsonSolid | title2=Johnson Solid| urlname=ParabiaugmentedDodecahedron  | title=Parabiaugmented dodecahedron }}

[[Category:Johnson solids]]

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