Triaugmented dodecahedron

{{Short description|61st Johnson solid}}

{{Infobox polyhedron

|image=triaugmented_dodecahedron.png

|type=Johnson
{{math|metabiaugmented dodecahedron – J{{sub|61}} – metabidiminished icosahedron}}

|faces=3+2×6 triangles
3×3 pentagons

|edges=45

|vertices=23

|symmetry={{math|C{{sub|3v}}}}

|vertex_config={{math|2+3(5{{sup|3}})
3+2.6(3{{sup|2}}.5{{sup|2}})
3(3{{sup|5}})}}

|dual=-

|properties=convex

|net=Johnson solid 61 net.png

}}

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

{{Johnson solid}}