Augmented dodecahedron

{{Short description|58th Johnson solid}}

{{Infobox polyhedron

|image=augmented_dodecahedron.png

|type=Johnson
{{math|triaugmented hexagonal prism – J{{sub|58}} – parabiaugmented dodecahedron}}

|faces=5 triangles
11 pentagons

|edges=35

|vertices=21

|symmetry={{math|C{{sub|5v}}}}

|vertex_config={{math|3.5(5{{sup|3}})
5(3{{sup|2}}.5{{sup|2}})
1(3{{sup|5}})}}

|dual=-

|properties=convex

|net=Johnson solid 58 net.png

}}

In geometry, the augmented dodecahedron is one of the Johnson solids ({{math|J{{sub|58}}}}), consisting of a dodecahedron with a pentagonal pyramid ({{math|J{{sub|2}}}}) attached to one of the faces. When two or three such pyramids are attached, the result may be a parabiaugmented dodecahedron ({{math|J{{sub|59}}}}), a metabiaugmented dodecahedron ({{math|J{{sub|60}}}}), or a triaugmented dodecahedron ({{math|J{{sub|61}}}}).

{{Johnson solid}}