parabiaugmented dodecahedron

{{Short description|59th Johnson solid}}

{{Infobox polyhedron

|image=parabiaugmented_dodecahedron.png

|type=Johnson
{{math|augmented dodecahedron – J{{sub|59}} – metabiaugmented dodecahedron}}

|faces=10 triangles
10 pentagons

|edges=40

|vertices=22

|symmetry={{math|D{{sub|5d}}}}

|vertex_config={{math|10(5{{sup|3}})
10(3{{sup|2}}.5{{sup|2}})
2(3{{sup|5}})}}

|dual=Gyroelongated pentagonal bifrustum

|properties=convex

|net=Johnson solid 59 net.png

}}

In geometry, the parabiaugmented dodecahedron is one of the Johnson solids ({{math|J{{sub|59}}}}). It can be seen as a dodecahedron with two pentagonal pyramids ({{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}}