Parabigyrate rhombicosidodecahedron

{{Short description|73rd Johnson solid}}

{{Infobox polyhedron

|image=parabigyrate_rhombicosidodecahedron.png

|type=Johnson
{{math|gyrate rhombicosidodecahedron – J{{sub|73}} – metabigyrate rhombicosidodecahedron}}

|faces=2x10 triangles
3x10 squares
2+10 pentagons

|edges=120

|vertices=60

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

|vertex_config={{math|20(3.4{{sup|2}}.5)
2x10+20(3.4.5.4)}}

|dual=-

|properties=convex, canonical

|net=Johnson solid 73 net.png

}}

In geometry, the parabigyrate rhombicosidodecahedron is one of the Johnson solids ({{math|J{{sub|73}}}}). It can be constructed as a rhombicosidodecahedron with two opposing pentagonal cupolae rotated through 36 degrees. It is also a canonical polyhedron.

{{Johnson solid}}

Alternative Johnson solids, constructed by rotating different cupolae of a rhombicosidodecahedron, are:

• The gyrate rhombicosidodecahedron ({{math|J{{sub|72}}}}) where only one cupola is rotated;
• The metabigyrate rhombicosidodecahedron ({{math|J{{sub|74}}}}) where two non-opposing cupolae are rotated;
• And the trigyrate rhombicosidodecahedron ({{math|J{{sub|75}}}}) where three cupolae are rotated.