Gyrate bidiminished rhombicosidodecahedron

{{Short description|82nd Johnson solid}}

{{Infobox polyhedron

|image=gyrate_bidiminished_rhombicosidodecahedron.png

|type=Johnson
{{math|metabidiminished rhombicosidodecahedron – J{{sub|82}} – tridiminished rhombicosidodecahedron}}

|faces=10 triangles
20 squares
10 pentagons
2 decagons

|edges=90

|vertices=50

|symmetry={{math|C{{sub|s}}}}

|vertex_config={{math|10.2(4.5.10)
5x2(3.4{{sup|2}}.5)
4+8.2(3.4.5.4)}}

|dual=-

|properties=Convex

|net=Johnson solid 82 net.png

}}

In geometry, the gyrate bidiminished rhombicosidodecahedron is one of the Johnson solids ({{math|J{{sub|82}}}}).

{{Johnson solid}}

It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae ({{math|J{{sub|5}}}}) removed and a third is rotated 36 degrees. Related Johnson solids are:

• The diminished rhombicosidodecahedron ({{math|J{{sub|76}}}}) where one cupola is removed,
• The parabidiminished rhombicosidodecahedron ({{math|J{{sub|80}}}}) where two opposing cupolae are removed,
• The metabidiminished rhombicosidodecahedron ({{math|J{{sub|81}}}}) where two non-opposing cupolae are removed,
• And the tridiminished rhombicosidodecahedron ({{math|J{{sub|83}}}}) where three cupolae are removed.