diminished rhombicosidodecahedron

{{Short description|76th Johnson solid}}

{{Infobox polyhedron

|image=diminished_rhombicosidodecahedron.png

|type=Johnson
{{math|trigyrate rhombicosidodecahedron – J{{sub|76}} – paragyrate diminished rhombicosidodecahedron}}

|faces=3x5 triangles
3x5+10 squares
1+2x5 pentagons
1 decagon

|edges=105

|vertices=55

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

|vertex_config={{math|10(4.5.10)
3x5+3x10(3.4.5.4)}}

|dual=-

|properties=convex

|net=Johnson solid 76 net.png

}}

In geometry, the diminished rhombicosidodecahedron is one of the Johnson solids ({{math|J{{sub|76}}}}). It can be constructed as a rhombicosidodecahedron with one pentagonal cupola removed.

{{Johnson solid}}

Related Johnson solids are:

• {{math|J{{sub|80}}}}: parabidiminished rhombicosidodecahedron with two opposing cupolae removed, and
• {{math|J{{sub|81}}}}: metabidiminished rhombicosidodecahedron with two non-opposing cupolae removed, and
• {{math|J{{sub|83}}}}: tridiminished rhombicosidodecahedron with three cupola removed.