triaugmented truncated dodecahedron

{{Short description|71st Johnson solid}}

{{Infobox polyhedron

|image=triaugmented_truncated_dodecahedron.png

|type=Johnson
{{math|metabiaugmented truncated dodecahedron – J{{sub|71}} – gyrate rhombicosidodecahedron}}

|faces=2+3x3+4x6 triangles
3+2x6 squares
3 pentagons
3x3 decagons

|edges=135

|vertices=75

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

|vertex_config={{math|4x3+3x6(3.10{{sup|2}})
3+2x6(3.4.5.4)
5x6(3.4.3.10)}}

|dual=-

|properties=convex

|net=Johnson solid 71 net.png

}}

In geometry, the triaugmented truncated dodecahedron is one of the Johnson solids ({{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 cupolas ({{math|J{{sub|5}}}}) onto three nonadjacent decagonal faces of a truncated dodecahedron.

{{Johnson solid}}